Derivative of a Product

Find the slope of the graph of the function at the given value.

f(x)=4(-4x+4)² at x = 3.

• f '(3) = -16

• f '(3) = - 64

• f '(3) = 256

• f '(3) = 64

Find the derivative of the function

f (x) = (x⁴ - 8) / x³

• f'(x) = 1 + 3/x⁴

• f'(x) = 1 - 8/x⁴

• f'(x) = 1 - 24/x⁴

• f'(x) = 1 + 24/x⁴

Find the derivative of f (x) = (x⁶ - 5)(x⁴ + 3)

• f'(x) = 10x⁹ + 20x⁵ -18x³

• f'(x) = 10x⁹ + 18x⁵ + 20x³

• f'(x) = 10x⁹ + 18x⁵ - 20x³

• f'(x) = 10x⁹ - 18x⁵ - 20x³

Differentiate the function.

f (t) = t⁵cos(t)

• f'(t) = -t⁵cos(t) + 5t⁴sin(t)

• f'(t) = -t⁵sin(t) - 5t⁴cos(t)

• f'(t) = t⁵sin(t) + 5t⁴cos(t)

• f'(t) = -t⁵sin(t) + 5t⁴cos(t)

Find an equation of the tangent line to the graph of the function at the given point.

f (v) = (v - 4)(v² - 6) at (3, -3)

• y = 3v + 6

• y = 12v - 3

• y = -3v -12

• y = - 3v + 6

Determine all values of x, (if any), at which the graph of the function has a horizontal tangent.

g(x) = x⁴ - 4x + 9

• x = 0 and x = 1

• x = 1

• x = 0

• x = 0 and x = -1

Find the derivative of the function.

p (x) = 7x (sin x) + 4 (cos x)

• p ' (x) = 7x(cos x) + 3(sin x)

• p ' (x) = 7x(sin x) - 3(cos x)

• p ' (x) = 7x(sin x) - 7(cos x)

• p ' (x) = -7x(sin x) + 3(cos x)