# Calculus Derivative Rules Practice

## 11 questions

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• Multiple Choice
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3 minutes
1 pt

If

$If\ y=\left(x^3+1\right)^2,\ then\ \frac{dy}{dx}=$

$\left(3x^2\right)^2$

$2\left(x^3+1\right)$

$2\left(3x^2+1\right)$

$3x^2\left(x^3+1\right)$

$6x^2\left(x^3+1\right)$

• Multiple Choice
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3 minutes
1 pt

$If\ g\left(x\right)=\frac{x-2}{x+2},\ then\ g'\left(2\right)=$

1

-1

1/4

-1/4

0

• Multiple Choice
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3 minutes
1 pt

Find the derivative of the following:

$\sqrt{x}-\frac{1}{x^{\frac{4}{3}}}$

$\frac{1}{2}x^{-\frac{1}{2}}-x^{-\frac{4}{3}}$

$\frac{1}{2}x^{-\frac{1}{2}}+\frac{4}{3}x^{-\frac{7}{3}}$

$\frac{1}{2}x^{-\frac{1}{2}}-\frac{4}{3}x^{-\frac{1}{3}}$

$-\frac{1}{2}x^{-\frac{1}{2}}+\frac{4}{3}x^{-\frac{7}{3}}$

$-\frac{1}{2}x^{-\frac{1}{2}}-\frac{4}{3}x^{-\frac{1}{3}}$

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