Using radians, let h(x) = x sin x. Find h'(pi/2).

For h(x) = (x+1)(x+2), find h'(1).

For the product 5x, multiplying the derivatives of the factors 5 and x gives its correct derivative.

Using radians, what is the derivative of x²sin x?

• 2x sin x+x²cos x
• 2x cos x+x²sin x
• 2x sin x-x²cos x

For h(x) = (2x+3)/(x-1), find h'(2).

For x distinct from 2, h(x) = (x²-4)/(x-2). What is h'(x) on its domain?

• 1
• x+2
• 2x
• 0

For h(x) = (x+2)/(x+3), find h'(-2).

At a point, differentiable f and g have f = 2, f' = -1, g = 4 and g' = 3. What is the derivative of f/g there?

• 5/8
• -5/4
• 1/8
• -5/8

Differentiable functions satisfy f(2) = 3, f'(2) = 1, g(2) = 4 and g'(2) = 5. Find (fg)'(2).

Using radians, what is the derivative of x cos x?

• cos x+x sin x
• cos x-sin x
• cos x-x sin x