Derivative Review

_{Estimate the slope of the tangent line at point A.}

• Undefined
• Zero
• 3
• -3

If f(x) = ln (2x), then f'(x) =

• 1/2x 
• 1/x
• 2x
• x

Find the derivative for
 f(x) = sin (2x³)

• f'(x)=cos(2x³)
• f'(x)=6x² cos (2x³)
• f'(x)=-cos(2x³)
• f'(x)=-6x² cos(2x³)

Evaluate the derivative at x = pi

• -1 - 3/(pi³)
• 9/(pi⁴)
• 3/(pi⁴)
• 9

Find the derivative.

• x⁴ cosx - 4x³ sinx
• x⁴ cosx + 4x³ sinx
• 4x³cosx
• -4x³cosx

Find the derivative.

• (x-9)(x+1)/(x-4)²
• (3x²-8x+9)/(x-4)²
• 2x
• 1/(2x)

If y = 2e^(5x) then find y'

• 2e^(5x)
• 10e^5x
• 2xe^(5x)
• 10xe^(5x)

Find f ' (1)

• 1

• -3

• 1/3

• -1/3

Find the slope of the tangent line to the function f(x) = 1/x³ at the point (2,-3)

• -1/8
• -3/16
• -48
• 1/4

When we "take the derivative" of a function what are we finding?

• What's a derivative?
• The rate at which our struggles in Calculus are increasing.
• The slope of the secant line
• The slope of the tangent line