Derivative Practice

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)

Find the derivative.
 f(z) = 1/(3z²) + 4z³

• f'(z) = 6z³ + 12z²

• f'(z) = 6z + 12x²

• f'(z) =  -2/(3z³) + 12z²

• f'(z) = -6/z² + 12z²

Set up the derivative of y=(3x⁴ - 7)*(5x² + 1)

• (12x³)*(10x)

• (3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)

• (3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)

• (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

• A

• B

• C

• D

Find the derivative of g(x)=(3x-2)/(x²+2)

• 9x²+2

• 3(x²+2)/(x²+2)²

• (-3x²+4x +6)/(x²+2)²

• (-3x²+10)/(x²+2)²

What is f'(x) if f(x) = cos(5x⁴)?

• f'(x) = sin(20x³)

• f'(x) = 20x³ sin(5x⁴)

• f'(x) = -sin(20x³)

• f'(x) = -20x³ sin(5x⁴)

.

• (3x²-2)cos(x³-2x)

• -(3x²-2)cos(x³-2x)

• cos(2x²-2)

• sin(2x²-2)

Hint: Split the fraction (Easier than quotient rule)

• A

• B

• C

• D

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

• m = 0

• f'(x) = -6x - 6

• f'(x) = 6x

• m = -12

If a function has a derivative that is negative, what does that tell you?

• The function is increasing

• The function is decreasing

• There is a max where it is negative

• There is a min where it is negative