For f(x) = (x²+1)³, find f'(1).

If g'(a) = 0 and f is differentiable at g(a), then the derivative of f(g(x)) at a is zero.

Using radians, f(x) = cos(5x). Find f'(0).

Differentiate (3x²+1)⁵ and identify its inner and outer functions.

• 30x(3x²+1)⁴; inner 3x²+1; outer u⁵
• 5(3x²+1)⁴; inner 3x²+1; outer u⁵
• 30x(3x²+1)⁵; inner 3x²+1; outer u⁵

y and x are in metres and t is in seconds. If dy/dx = 2 and dx/dt = 3, what is dy/dt?

• 6 metres per second
• 6 metres per metre
• 6 seconds per metre

To obtain a circle's area rate from A = pi r², substitute its momentary radius as a constant before differentiating in time.

A sphere has radius 3 cm and volume rate 72pi cm³/s. With V = (4/3)pi r³, what is its radius rate?

• 2 cm/s
• 6 cm/s
• 8 cm/s

Using radians, what is the derivative of e^(cos(4x))?

• 4cos(4x)e^(cos(4x))
• -4sin(4x)e^(cos(4x))
• -sin(4x)e^(cos(4x))

Using radians, f(x) = e^(sin(x²)). Find f'(0).

A sphere has radius 3 cm increasing at 0.5 cm/s. With V = (4/3)pi r³, what is its volume rate?

• 9pi cm³/s
• 18pi cm³/s
• 4.5pi cm³/s