Question 1

Find the value of the derivative of $y=\frac{3 x+2}{\sqrt{x+1}}$ at $x=2$. Give an exact answer.

Accepted Answer

The answer of Find the value of the derivative of...

Question 2

Using the delta method, find the instantaneous rate of change of the function at the given value of $x$ :
$y=\frac{x^{2}+1}{x} at x=2$

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The answer of Using the delta method, find the instantaneous...

Question 3

Given $f(x)=x^{2}-x^{3}$, find $f^{\prime \prime}(0.25)$.

Accepted Answer

The answer of Given $f(x)=x^{2}-x^{3}$, find $f^{\prime \prime}(0.25)$....

Question 4

Find the derivative: $y=(2 x-1) \sqrt{3-4 x}$

Accepted Answer

The answer of Find the derivative: $y=(2 x-1) \sqrt{3-4 x}$...

Question 5

Find the derivative of: $y=7 x^{3}(2 x+1)^{4}$

Accepted Answer

The answer of Find the derivative of: $y=7 x^{3}(2 x+1)^{4}$...

Question 6

If $y=\frac{1}{\left(x^{2}-2\right)^{3}}$, find $y^{\prime}(-3$.$) .$

Accepted Answer

The answer of If $y=\frac{1}{\left(x^{2}-2\right)^{3}}$, find $y^{\prime}(-3$.$) .$...

Question 7

Find the derivative:
$y=4 x^{3}+8 \sqrt{x}-\frac{2}{x^{2}}+25$

Accepted Answer

The answer of Find the derivative:
$y=4 x^{3}+8 \sqrt{x}-\frac{2}{x^{2}}+25$...

Question 8

Evaluate the limit:
$\lim _{\pi/2}{\frac{\cos x}{\cot x}}$

Accepted Answer

The answer of Evaluate the limit:
$\lim _{\pi/2}{\frac{\cos x}{\cot x}}$...

Question 9

Evaluate the limit:
$\lim_{x\rightarrow 2}{\frac{x^{4}-16}{x-2}}$

Accepted Answer

The answer of Evaluate the limit:
$\lim_{x\rightarrow 2}{\frac{x^{4}-16}{x-2}}$...

Question 10

Find the derivative: $y=9 x^{4}(8-x)^{7}$

Accepted Answer

The answer of Find the derivative: $y=9 x^{4}(8-x)^{7}$...

Question 11

Find the derivative: $y=\frac{3}{\sqrt[4]{x}}$

Accepted Answer

The answer of Find the derivative: $y=\frac{3}{\sqrt[4]{x}}$...

Question 12

If $z=\left(w^{2}+2 w\right)^{3}$, find $\frac{d z}{d x}$.

Accepted Answer

The answer of If $z=\left(w^{2}+2 w\right)^{3}$, find $\frac{d z}{d x}$....

Question 13

Evaluate the limit: 
$\lim _{x \rightarrow 2^{+}} \frac{2 x+3}{x-2}$

Accepted Answer

The answer of Evaluate the limit: 
\(\lim _{x \rightarrow 2^{+}}...

Question 14

Find the derivative: $y=\sqrt[3]{\left(\frac{3}{x}-x^{3}\right)^{2}}$

Accepted Answer

The answer of Find the derivative: $y=\sqrt[3]{\left(\frac{3}{x}-x^{3}\right)^{2}}$...

Question 15

Find the derivative: $y=(x-2)^{2}$

Accepted Answer

The answer of Find the derivative: $y=(x-2)^{2}$...

Question 16

Find $\frac{d y}{d x}: y=\frac{x}{\sqrt{x}}+x^{2}$

Accepted Answer

The answer of Find $\frac{d y}{d x}: y=\frac{x}{\sqrt{x}}+x^{2}$...

Question 17

Evaluate the limit: $\lim _{x \rightarrow 3} \frac{9-x^{2}}{x-3}$

Accepted Answer

The answer of Evaluate the limit: \(\lim _{x \rightarrow 3}...

Question 18

Evaluate the limit: $\lim_{x \rightarrow 0}(2x^2 - 9x + 5)$

Accepted Answer

The answer of Evaluate the limit: \(\lim_{x \rightarrow 0}(2x^2 -...

Question 19

Find the third derivative: $y=\sqrt{(2 x+1)^{3}}$

Accepted Answer

The answer of Find the third derivative: $y=\sqrt{(2 x+1)^{3}}$...

Question 20

Given $f(x)=4 x^{2}-\frac{5}{x}$, find $f^{\prime}(2)$.

Accepted Answer

The answer of Given $f(x)=4 x^{2}-\frac{5}{x}$, find $f^{\prime}(2)$....

Exam 27: Derivatives of Algebraic Functions

If z=(w2+2w)3z=\left(w^{2}+2 w\right)^{3}z=(w2+2w)3 , find dzdx\frac{d z}{d x}dxdz​ .

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Evaluate the limit: lim⁡x→39−x2x−3\lim _{x \rightarrow 3} \frac{9-x^{2}}{x-3}limx→3​x−39−x2​

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Given f(x)=x2−x3f(x)=x^{2}-x^{3}f(x)=x2−x3 , find f′′(0.25)f^{\prime \prime}(0.25)f′′(0.25) .

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Evaluate the limit: lim⁡π/2cos⁡xcot⁡x\lim _{\pi/2}{\frac{\cos x}{\cot x}}limπ/2​cotxcosx​

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Find the third derivative: y=(2x+1)3y=\sqrt{(2 x+1)^{3}}y=(2x+1)3​

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Find the derivative: y=4x3+8x−2x2+25y=4 x^{3}+8 \sqrt{x}-\frac{2}{x^{2}}+25y=4x3+8x​−x22​+25

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Find the derivative: y=(x−2)2y=(x-2)^{2}y=(x−2)2

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Find the derivative of: y=7x3(2x+1)4y=7 x^{3}(2 x+1)^{4}y=7x3(2x+1)4

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Find the derivative: y=(2x−1)3−4xy=(2 x-1) \sqrt{3-4 x}y=(2x−1)3−4x​

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Find the derivative: y=(3x−x3)23y=\sqrt[3]{\left(\frac{3}{x}-x^{3}\right)^{2}}y=3(x3​−x3)2​

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Evaluate the limit: lim⁡x→0(2x2−9x+5)\lim_{x \rightarrow 0}(2x^2 - 9x + 5)limx→0​(2x2−9x+5)

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Find the value of the derivative of y=3x+2x+1y=\frac{3 x+2}{\sqrt{x+1}}y=x+1​3x+2​ at x=2x=2x=2 . Give an exact answer.

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If y=1(x2−2)3y=\frac{1}{\left(x^{2}-2\right)^{3}}y=(x2−2)31​ , find y′(−3y^{\prime}(-3y′(−3 . ).) .).

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Find the derivative: y=9x4(8−x)7y=9 x^{4}(8-x)^{7}y=9x4(8−x)7

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Find dydx:y=xx+x2\frac{d y}{d x}: y=\frac{x}{\sqrt{x}}+x^{2}dxdy​:y=x​x​+x2

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Evaluate the limit: lim⁡x→2+2x+3x−2\lim _{x \rightarrow 2^{+}} \frac{2 x+3}{x-2}limx→2+​x−22x+3​

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Given f(x)=4x2−5xf(x)=4 x^{2}-\frac{5}{x}f(x)=4x2−x5​ , find f′(2)f^{\prime}(2)f′(2) .

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Evaluate the limit: lim⁡x→2x4−16x−2\lim_{x\rightarrow 2}{\frac{x^{4}-16}{x-2}}limx→2​x−2x4−16​

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Using the delta method, find the instantaneous rate of change of the function at the given value of xxx : y=x2+1xatx=2y=\frac{x^{2}+1}{x} at x=2y=xx2+1​atx=2

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Find the derivative: y=3x4y=\frac{3}{\sqrt[4]{x}}y=4x​3​

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If $z=\left(w^{2}+2 w\right)^{3}$ , find $\frac{d z}{d x}$ .

Correct Answer
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Evaluate the limit: $\lim _{x \rightarrow 3} \frac{9-x^{2}}{x-3}$

Correct Answer
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Given $f(x)=x^{2}-x^{3}$ , find $f^{\prime \prime}(0.25)$ .

Correct Answer
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Evaluate the limit: $\lim _{\pi/2}{\frac{\cos x}{\cot x}}$

Correct Answer
verified

Find the third derivative: $y=\sqrt{(2 x+1)^{3}}$

Correct Answer
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Find the derivative: $y=4 x^{3}+8 \sqrt{x}-\frac{2}{x^{2}}+25$

Correct Answer
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Find the derivative: $y=(x-2)^{2}$

Correct Answer
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Find the derivative of: $y=7 x^{3}(2 x+1)^{4}$

Correct Answer
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Find the derivative: $y=(2 x-1) \sqrt{3-4 x}$

Correct Answer
verified

Find the derivative: $y=\sqrt[3]{\left(\frac{3}{x}-x^{3}\right)^{2}}$

Correct Answer
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Evaluate the limit: $\lim_{x \rightarrow 0}(2x^2 - 9x + 5)$

Correct Answer
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Find the value of the derivative of $y=\frac{3 x+2}{\sqrt{x+1}}$ at $x=2$ . Give an exact answer.

Correct Answer
verified

If $y=\frac{1}{\left(x^{2}-2\right)^{3}}$ , find $y^{\prime}(-3$ . $) .$

Correct Answer
verified

Find the derivative: $y=9 x^{4}(8-x)^{7}$

Correct Answer
verified

Find $\frac{d y}{d x}: y=\frac{x}{\sqrt{x}}+x^{2}$

Correct Answer
verified

Evaluate the limit: $\lim _{x \rightarrow 2^{+}} \frac{2 x+3}{x-2}$

Correct Answer
verified

Given $f(x)=4 x^{2}-\frac{5}{x}$ , find $f^{\prime}(2)$ .

Correct Answer
verified

Evaluate the limit: $\lim_{x\rightarrow 2}{\frac{x^{4}-16}{x-2}}$

Correct Answer
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Using the delta method, find the instantaneous rate of change of the function at the given value of $x$ : $y=\frac{x^{2}+1}{x} at x=2$

Correct Answer
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Find the derivative: $y=\frac{3}{\sqrt[4]{x}}$

Correct Answer
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