Question 1

Find the derivative of  h(t) =tπ4+(π4) t+πt4h ( t )  = t ^ { \pi ^ { 4 } } + \left( \pi ^ { 4 } \right)  ^ { t } + \pi t ^ { 4 }h(t) =tπ4+(π4) t+πt4  .

Accepted Answer

A)    π4t(π4−1) +t(π4) t−1+4πt3\pi ^ { 4 } t ^ { \left( \pi ^ { 4 } - 1 \right)  } + t \left( \pi ^ { 4 } \right)  ^ { t - 1 } + 4 \pi t ^ { 3 }π4t(π4−1) +t(π4) t−1+4πt3 
B)    π4t(π4−1) +(π4) +ln⁡(π4) +4π3\pi ^ { 4 } t ^ { \left( \pi ^ { 4 } - 1 \right)  } + \left( \pi ^ { 4 } \right)  ^ { + } \ln \left( \pi ^ { 4 } \right)  + 4 \pi ^ { 3 }π4t(π4−1) +(π4) +ln(π4) +4π3 
C)    t(π4−1) ln⁡t+(π4) tln⁡(π4) +4πt4ln⁡tt ^ { \left( \pi ^ { 4 } - 1 \right)  } \ln t + \left( \pi ^ { 4 } \right)  ^ { t } \ln \left( \pi ^ { 4 } \right)  + 4 \pi t ^ { 4 } \ln tt(π4−1) lnt+(π4) tln(π4) +4πt4lnt 
D)    4tπ3+4t(π3) t−1+4πt4ln⁡t4 t ^ { \pi ^ { 3 } } + 4 t \left( \pi ^ { 3 } \right)  ^ { t - 1 } + 4 \pi t ^ { 4 } \ln t4tπ3+4t(π3) t−1+4πt4lnt

Question 2

With a yearly inflation rate of 7%, prices are described by $P = P _ { 0 } ( 1.07 ) ^ { \dagger }$ , where $P _ { 0 }$ is the price in dollars when t = 0 and t is time in years.If $P _ { 0 }$ = 1.3, how fast (in cents/year)are prices rising when t = 19? Round to 1 decimal place.

Accepted Answer

The answer of With a yearly inflation rate of 7%,...

Question 3

Find a differentiation formula for $y = \cot ( \theta )$ .

Accepted Answer

The answer of Find a differentiation formula for \(y =...

Question 4

Use the product rule to write a proof of the constant multiple rule: $\frac { d } { d x } c f ( x ) = c \frac { d } { d } f ( x )$ .

Accepted Answer

Let c be any constan...

Question 5

Find  ddx(1+89x) \frac { d } { d x } \left( \sqrt { 1 + 8 ^ { 9 x } } \right) dxd​(1+89x​)   .

Accepted Answer

A)    9⋅ln⁡8⋅89x\sqrt { 9 \cdot \ln 8 \cdot 8 ^ { 9 x } }9⋅ln8⋅89xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
B)    9x⋅89x−1\sqrt { 9 x \cdot 8 ^ { 9 x - 1 } }9x⋅89x−1c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    9⋅ln⁡8⋅89x21+89x\frac { 9 \cdot \ln 8 \cdot 8 ^ { 9 x } } { 2 \sqrt { 1 + 8 ^ { 9 x } } }21+89xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​9⋅ln8⋅89x​ 
D)    9x⋅89x−121+89x\frac { 9 x \cdot 8 ^ { 9 x - 1 } } { 2 \sqrt { 1 + 8 ^ { 9 x } } }21+89xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​9x⋅89x−1​

Question 6

Find the exact slope of the tangent line to $y = \sinh x$ when x = 1.

Accepted Answer

The answer of Find the exact slope of the tangent...

Question 7

Find the critical number(s)of the curve $y = a e ^ { b x } \left( 1 - e ^ { b x } \right)$ .

Accepted Answer

The answer of Find the critical number(s)of the curve \(y...

Question 8

Differentiate  h(θ) =5θsin⁡(θ2) h ( 	heta )  = 5 	heta \sin \left( 	heta ^ { 2 } ight) h(θ) =5θsin(θ2)   .

Accepted Answer

A)    5cos⁡(2θ) 5 \cos ( 2 	heta ) 5cos(2θ)  
B)    5θcos⁡(θ2) +5sin⁡(θ2) 5 	heta \cos \left( 	heta ^ { 2 } ight)  + 5 \sin \left( 	heta ^ { 2 } ight) 5θcos(θ2) +5sin(θ2)  
C)    10θ2cos⁡(θ2) +5sin⁡(θ2) 10 	heta ^ { 2 } \cos \left( 	heta ^ { 2 } ight)  + 5 \sin \left( 	heta ^ { 2 } ight) 10θ2cos(θ2) +5sin(θ2)  
D)    −10θ2cos⁡(θ2) +sin⁡(θ2) - 10 	heta ^ { 2 } \cos \left( 	heta ^ { 2 } ight)  + \sin \left( 	heta ^ { 2 } ight) −10θ2cos(θ2) +sin(θ2)

Question 9

Consider the following table of data for the function f.
 $$\begin{array} { c c c c c c } 
x & 5.0 & 5.1 & 5.2 & 5.3 & 5.4 \
f ( x ) & 9.2 & 8.8 & 8.3 & 7.7 & 7.0
\end{array}$$ Suppose g is a function such that g(5.1)= 9 and g'(5.1)= 3.Find h'(5.1)where h(x)= f(x)g(x).Use the right-hand estimate for $f ^ { \prime } ( 5.1 )$ .Round to 2 decimal places.

Accepted Answer

The answer of Consider the following table of data for...

Question 10

What is the instantaneous rate of change of the function $f ( x ) = e ^ { - x ^ { 2 } }$ at x = 2? Round to 3 decimal places.

Accepted Answer

The answer of What is the instantaneous rate of change...

Question 11

Differentiate  f(y) =ln⁡(2+y2−y) f ( y )  = \ln \left( \frac { 2 + y } { 2 - y } \right) f(y) =ln(2−y2+y​)   .

Accepted Answer

A)    2−y2+y\frac { 2 - y } { 2 + y }2+y2−y​ 
B)    −2−y2+y- \frac { 2 - y } { 2 + y }−2+y2−y​ 
C)    4(2−y) 2\frac { 4 } { ( 2 - y )  ^ { 2 } }(2−y) 24​ 
D)    4(2+y) (2−y) \frac { 4 } { ( 2 + y )  ( 2 - y )  }(2+y) (2−y) 4​

Question 12

The derivative of $\sin \frac { 2 } { x }$ is $2 \cos \frac { 2 } { x }$ .

Accepted Answer

A) True 
 B)False

Question 13

Given  f(x) =exf ( x )  = e ^ { x }f(x) =ex  ,  g(x) =5xg ( x )  = 5 ^ { x }g(x) =5x  , and h(x) = g(x) /f(x) , find  h′′(x) h ^ { \prime \prime } ( x ) h′′(x)   .

Accepted Answer

A)    5xe−x(ln⁡5+1) 25 ^ { x } e ^ { - x } ( \ln 5 + 1 )  ^ { 2 }5xe−x(ln5+1) 2 
B)    5xe−x(ln⁡5−1) 25 ^ { x } e ^ { - x } ( \ln 5 - 1 )  ^ { 2 }5xe−x(ln5−1) 2 
C)    5xe−x(ln⁡5) 25 ^ { x } e ^ { - x } ( \ln 5 )  ^ { 2 }5xe−x(ln5) 2 
D)    −x(x−1) 5x−2e−x−2(ln⁡5) 2- x ( x - 1 )  5 ^ { x - 2 } e ^ { - x - 2 } ( \ln 5 )  ^ { 2 }−x(x−1) 5x−2e−x−2(ln5) 2

Question 14

Differentiate  ddx[7e2x2+8x]\frac { d } { d x } \left[ 7 e ^ { 2 x ^ { 2 } + 8 x } \right]dxd​[7e2x2+8x]  .

Accepted Answer

A)    7(4x+8) e2x2+8x7 ( 4 x + 8 )  e ^ { 2 x ^ { 2 } + 8 x }7(4x+8) e2x2+8x 
B)    7e2x2+8x7 e ^ { 2 x ^ { 2 } + 8 x }7e2x2+8x 
C)    7ln⁡(2x2+8x) e2x2+8x7 \ln \left( 2 x ^ { 2 } + 8 x \right)  e ^ { 2 x ^ { 2 } + 8 x }7ln(2x2+8x) e2x2+8x 
D)    7(2x2+8x) e2x2+8x−17 \left( 2 x ^ { 2 } + 8 x \right)  e ^ { 2 x ^ { 2 } + 8 x - 1 }7(2x2+8x) e2x2+8x−1

Question 15

Find the derivative of  g(x) =3x−1x3+3xg ( x )  = 3 x - \frac { 1 } { \sqrt [ 3 ] { x } } + 3 ^ { x }g(x) =3x−3x​1​+3x  .

Accepted Answer

A)    3+13x4/3+(ln⁡3) 3x3 + \frac { 1 } { 3 x ^ { 4 / 3 } } + ( \ln 3 )  3 ^ { x }3+3x4/31​+(ln3) 3x 
B)    3−13x4/3+(ln⁡3) 3x3 - \frac { 1 } { 3 x ^ { 4 / 3 } } + ( \ln 3 )  3 ^ { x }3−3x4/31​+(ln3) 3x 
C)    3+13x+x3x−13 + \frac { 1 } { 3 \sqrt { x } } + x 3 ^ { x - 1 }3+3xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​1​+x3x−1 
D)    3−13x+x3x−13 - \frac { 1 } { 3 \sqrt { x } } + x 3 ^ { x - 1 }3−3xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​1​+x3x−1

Question 16

Given $y = 4 ^ { x } + 5 ^ { x }$ , find $y ^ { 111 }$ .

Accepted Answer

The answer of Given \(y = 4 ^ { x...

Question 17

A table of values for functions F and G near x = 3 is given below.If H(x)= F(x)/G(x), estimate H'(3)by using the quotient rule and then using right-hand estimates for $F ^ { \prime }$ and $G ^ { \prime }$ .Round to 2 decimal places.
 $$\begin{array} { c c c c } 
x & 2.9 & 3.0 & 3.1 \
F ( x ) & 7.7 & 8 & 8.3 \
G ( x ) & 2.2 & 2 & 1.8
\end{array}$$

Accepted Answer

The answer of A table of values for functions F...

Question 18

If p(x)= ln((x - a)(x - b)(x - c))and a, b, c are constants, then $p ^ { \prime } ( x ) = \frac { 1 } { x - a } + \frac { 1 } { x - b } + \frac { 1 } { x - c }$ .

Accepted Answer

A) True 
 B)False

Question 19

A particle moves in such a way that $x ( t ) = 2 t ^ { 2 } + 8 \sin t$ .What is the instantaneous rate of change at t = 0?

Accepted Answer

The answer of A particle moves in such a way...

Question 20

The volume of a certain tree is given by $V = \frac { 1 } { 12 \pi } C ^ { 2 } h$ , where C is the circumference of the tree at the ground level and h is the height of the tree.If C is 4 feet and growing at the rate of 0.25 feet per year, and if h is 25 feet and is growing at 5 feet per year, find the rate of growth of the volume V (in ft3/yr).Round to 2 decimal places.

Accepted Answer

Exam 3: Short-Cuts to Differentiation

Find the exact slope of the tangent line to $y = \sinh x$ when x = 1.

Correct Answer
verified

With a yearly inflation rate of 7%, prices are described by $P = P _ { 0 } ( 1.07 ) ^ { \dagger }$ , where $P _ { 0 }$ is the price in dollars when t = 0 and t is time in years.If $P _ { 0 }$ = 1.3, how fast (in cents/year)are prices rising when t = 19? Round to 1 decimal place.

Correct Answer
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A particle moves in such a way that $x ( t ) = 2 t ^ { 2 } + 8 \sin t$ .What is the instantaneous rate of change at t = 0?

Correct Answer
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What is the instantaneous rate of change of the function $f ( x ) = e ^ { - x ^ { 2 } }$ at x = 2? Round to 3 decimal places.

Correct Answer
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The derivative of $\sin \frac { 2 } { x }$ is $2 \cos \frac { 2 } { x }$ .

Correct Answer
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Correct Answer
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Given $f ( x ) = e ^ { x }$ , $g ( x ) = 5 ^ { x }$ , and h(x) = g(x) /f(x) , find $h ^ { \prime \prime } ( x )$ .

Correct Answer
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Differentiate $\frac { d } { d x } \left[ 7 e ^ { 2 x ^ { 2 } + 8 x } \right]$ .

Correct Answer
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Correct Answer
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Find a differentiation formula for $y = \cot ( \theta )$ .

Correct Answer
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Differentiate $h ( \theta ) = 5 \theta \sin \left( \theta ^ { 2 } \right)$ .

Correct Answer
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Differentiate $f ( y ) = \ln \left( \frac { 2 + y } { 2 - y } \right)$ .

Correct Answer
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Use the product rule to write a proof of the constant multiple rule: $\frac { d } { d x } c f ( x ) = c \frac { d } { d } f ( x )$ .

Correct Answer
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Let c be any constan...
View Answer

Find $\frac { d } { d x } \left( \sqrt { 1 + 8 ^ { 9 x } } \right)$ .

Correct Answer
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If p(x)= ln((x - a)(x - b)(x - c))and a, b, c are constants, then $p ^ { \prime } ( x ) = \frac { 1 } { x - a } + \frac { 1 } { x - b } + \frac { 1 } { x - c }$ .

Correct Answer
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Given $y = 4 ^ { x } + 5 ^ { x }$ , find $y ^ { 111 }$ .

Correct Answer
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Find the critical number(s)of the curve $y = a e ^ { b x } \left( 1 - e ^ { b x } \right)$ .

Correct Answer
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Correct Answer
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Find the derivative of $g ( x ) = 3 x - \frac { 1 } { \sqrt [ 3 ] { x } } + 3 ^ { x }$ .

Correct Answer
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Find the derivative of $h ( t ) = t ^ { \pi ^ { 4 } } + \left( \pi ^ { 4 } \right) ^ { t } + \pi t ^ { 4 }$ .

Correct Answer
verified

Exam 3: Short-Cuts to Differentiation

Find the exact slope of the tangent line to y=sinh⁡xy = \sinh xy=sinhx when x = 1.

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

A particle moves in such a way that x(t)=2t2+8sin⁡tx ( t ) = 2 t ^ { 2 } + 8 \sin tx(t)=2t2+8sint .What is the instantaneous rate of change at t = 0?

Correct AnswerverifiedShow Answer

What is the instantaneous rate of change of the function f(x)=e−x2f ( x ) = e ^ { - x ^ { 2 } }f(x)=e−x2 at x = 2? Round to 3 decimal places.

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The derivative of sin⁡2x\sin \frac { 2 } { x }sinx2​ is 2cos⁡2x2 \cos \frac { 2 } { x }2cosx2​ .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Given f(x) =exf ( x ) = e ^ { x }f(x) =ex , g(x) =5xg ( x ) = 5 ^ { x }g(x) =5x , and h(x) = g(x) /f(x) , find h′′(x) h ^ { \prime \prime } ( x ) h′′(x) .

Correct AnswerverifiedShow Answer

Differentiate ddx[7e2x2+8x]\frac { d } { d x } \left[ 7 e ^ { 2 x ^ { 2 } + 8 x } \right]dxd​[7e2x2+8x] .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find a differentiation formula for y=cot⁡(θ)y = \cot ( \theta )y=cot(θ) .

Correct AnswerverifiedShow Answer

Differentiate h(θ) =5θsin⁡(θ2) h ( \theta ) = 5 \theta \sin \left( \theta ^ { 2 } \right) h(θ) =5θsin(θ2) .

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Differentiate f(y) =ln⁡(2+y2−y) f ( y ) = \ln \left( \frac { 2 + y } { 2 - y } \right) f(y) =ln(2−y2+y​) .

Correct AnswerverifiedShow Answer

Use the product rule to write a proof of the constant multiple rule: ddxcf(x)=cddf(x)\frac { d } { d x } c f ( x ) = c \frac { d } { d } f ( x )dxd​cf(x)=cdd​f(x) .

Correct AnswerverifiedLet c be any constan...View AnswerShow Answer

Find ddx(1+89x) \frac { d } { d x } \left( \sqrt { 1 + 8 ^ { 9 x } } \right) dxd​(1+89x​) .

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If p(x)= ln((x - a)(x - b)(x - c))and a, b, c are constants, then p′(x)=1x−a+1x−b+1x−cp ^ { \prime } ( x ) = \frac { 1 } { x - a } + \frac { 1 } { x - b } + \frac { 1 } { x - c }p′(x)=x−a1​+x−b1​+x−c1​ .

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Given y=4x+5xy = 4 ^ { x } + 5 ^ { x }y=4x+5x , find y111y ^ { 111 }y111 .

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Find the critical number(s)of the curve y=aebx(1−ebx)y = a e ^ { b x } \left( 1 - e ^ { b x } \right)y=aebx(1−ebx) .

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find the derivative of g(x) =3x−1x3+3xg ( x ) = 3 x - \frac { 1 } { \sqrt [ 3 ] { x } } + 3 ^ { x }g(x) =3x−3x​1​+3x .

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Find the derivative of h(t) =tπ4+(π4) t+πt4h ( t ) = t ^ { \pi ^ { 4 } } + \left( \pi ^ { 4 } \right) ^ { t } + \pi t ^ { 4 }h(t) =tπ4+(π4) t+πt4 .

Correct AnswerverifiedShow Answer

Find the exact slope of the tangent line to $y = \sinh x$ when x = 1.

Correct Answer
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Correct Answer
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A particle moves in such a way that $x ( t ) = 2 t ^ { 2 } + 8 \sin t$ .What is the instantaneous rate of change at t = 0?

Correct Answer
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What is the instantaneous rate of change of the function $f ( x ) = e ^ { - x ^ { 2 } }$ at x = 2? Round to 3 decimal places.

Correct Answer
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The derivative of $\sin \frac { 2 } { x }$ is $2 \cos \frac { 2 } { x }$ .

Correct Answer
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Correct Answer
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Given $f ( x ) = e ^ { x }$ , $g ( x ) = 5 ^ { x }$ , and h(x) = g(x) /f(x) , find $h ^ { \prime \prime } ( x )$ .

Correct Answer
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Differentiate $\frac { d } { d x } \left[ 7 e ^ { 2 x ^ { 2 } + 8 x } \right]$ .

Correct Answer
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Correct Answer
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Find a differentiation formula for $y = \cot ( \theta )$ .

Correct Answer
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Differentiate $h ( \theta ) = 5 \theta \sin \left( \theta ^ { 2 } \right)$ .

Correct Answer
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Differentiate $f ( y ) = \ln \left( \frac { 2 + y } { 2 - y } \right)$ .

Correct Answer
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Use the product rule to write a proof of the constant multiple rule: $\frac { d } { d x } c f ( x ) = c \frac { d } { d } f ( x )$ .

Correct Answer
verified
Let c be any constan...
View Answer

Find $\frac { d } { d x } \left( \sqrt { 1 + 8 ^ { 9 x } } \right)$ .

Correct Answer
verified

If p(x)= ln((x - a)(x - b)(x - c))and a, b, c are constants, then $p ^ { \prime } ( x ) = \frac { 1 } { x - a } + \frac { 1 } { x - b } + \frac { 1 } { x - c }$ .

Correct Answer
verified

Given $y = 4 ^ { x } + 5 ^ { x }$ , find $y ^ { 111 }$ .

Correct Answer
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Find the critical number(s)of the curve $y = a e ^ { b x } \left( 1 - e ^ { b x } \right)$ .

Correct Answer
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Correct Answer
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Find the derivative of $g ( x ) = 3 x - \frac { 1 } { \sqrt [ 3 ] { x } } + 3 ^ { x }$ .

Correct Answer
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Find the derivative of $h ( t ) = t ^ { \pi ^ { 4 } } + \left( \pi ^ { 4 } \right) ^ { t } + \pi t ^ { 4 }$ .

Correct Answer
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