Calculus Derivative Rules Practice

If

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

•  $\left(3x^2\right)^2$  

•  $2\left(x^3+1\right)$  

•  $2\left(3x^2+1\right)$  

•  $3x^2\left(x^3+1\right)$  

•  $6x^2\left(x^3+1\right)$  

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

• 1

• -1
  

• 1/4

• -1/4

• 0

Find the derivative of the following:

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

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

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

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

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

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

Tags

CCSS.HSN.RN.A.2

Find f'(2) if

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

• -2

• 1/6

• 1/2

• 2

• 6

Let f be the function defined below. Which of the following is an equation of the line tangent to the graph of f at the point where x = -1?

 $f\left(x\right)=4x^3-5x+3$  

• y = -7x - 3

• y = 7x + 7

• y = 7x + 11

• y = -5x - 1

• y = -5x - 5

 $If\ y=\frac{3}{4+x^2},\ then\ \frac{dy}{dx}=$  

•  $\frac{3}{2x}$  

•  $\frac{3x}{\left(1+x^2\right)^2}$  

•  $\frac{6x}{\left(4+x^2\right)^2}$  

•  $-\frac{6x}{\left(4+x^2\right)^2}$  

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

If the line tangent to the graph of the function f at the point (1,7) passes through the point (-2, -2), then f'(1) =

• -5

• 1

• 3

• 7

• undefined

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Let f be a differentiable function with f(2) = 3 and f'(2) = -5, and let g be a function defined by g(x) = x ^. f(x). Which of the following is an equation of the line tangent to the graph of g at the point where x = 2?

• $y=3x$

• $y-3=-5\left(x-2\right)$

• $y-6=-5\left(x-2\right)$

• $y-6=-7\left(x-2\right)$

• $y-6=-10\left(x-2\right)$

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

If g'(-4) = 2 and h'(-4) = 3, find f'(-4) for

 $f\left(x\right)=4g\left(x\right)-6h\left(x\right)+3$  

• 29

• -10

• 26

• -7

• 1

 $If\ y=5x^3-6x^2+4,\ find\ \frac{\text{d}^2y}{\text{d}x^2}$  

• 30x - 12

• 12x - 20

• 12x - 30

• 20x - 12

•  $15x^2-12x$  

Tags

CCSS.HSA.APR.A.1