AP Calc Review Quiz #3

What is the derivative of a constant, C?

• C
• 1
• 0

Find the derivative of:

 $f\left(x\right)=\frac{2}{x^2}-\frac{9}{x}$  

•  $f'\left(x\right)=-\frac{4}{x^3}+\frac{9}{x^2}$  

•  $f'\left(x\right)=-\frac{4}{x}+9$  

•  $f'\left(x\right)=\frac{2}{x^3}-\frac{9}{x^2}$  

•  $f'\left(x\right)=\frac{4}{x^3}-\frac{9}{x^2}$  

Find the derivative of:

 $f\left(x\right)=4\sqrt{x}$  

•  $f'\left(x\right)=\frac{2}{\sqrt{x}}$  

•  $f'\left(x\right)=2\sqrt{x}$  

•  $f'\left(x\right)=4x^{\frac{1}{2}}$  

•  $f'\left(x\right)=2x^{-\frac{1}{2}}$  

Which option is using correctly the quotient rule?

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• 
• 
• 

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴
• f'(t) = 5(t² + 2t)⁴
•  f'(t) = 5(t² + 2t)⁴(2t)
• f'(t) = 5(t² + 2t)⁴(2t + 2)

Use the product rule to find the derivative. $f\left(x\right)\ =\ -x^3\left(3x^4-2\right)$  

•  $-3x^2+12x^3$  

•  $-21x^3+6x$  

•  $-21x^6+6x^2$  

•  $-84x^6-6x^2$  

Solve f '(2)  for 
f(x) = x² + 2x

• 2x + 2
• 6
• 12
• 2x

Tags

CCSS.HSF.IF.A.2

Find dy/dx if y = cos⁵x

• 5cos⁴x
• -5sin⁴x
• 5cos⁴xsinx
• -5cos⁴xsinx

 $\frac{\text{d}}{\text{d}x}\left[x^2\cdot\sin\left(x\right)\right]$  

•  $x^2\cos\left(x\right)-2x\left(\sin x\right)$  

•  $-x^2\sin\left(x\right)+2x\cos\left(x\right)$  

•  $x^2\sin\left(x\right)+2x\cos\left(x\right)$  

•  $x^2\cos\left(x\right)+2x\sin\left(x\right)$  

Find the slope of f(x) = -3x²-6x at x = 1.

• m = 0
• f'(x) = -6x - 6
• f'(x) = 6x
• m = -12

Tags

CCSS.8.EE.B.5