In Exercise, apply the three-step method to compute f′(x) for the given function. Follow t...

In Exercise, apply the three-step method to compute f′(x) for the given function. Follow the steps that we used in Example. Make sure to simplify the difference quotient as much as possible before taking limits.

f(x) = x3 – 1

Example

Computing Derivative from the Definition Find the derivative of f(x) = x2 + 2x + 2.

SOLUTION We have

Let us go back to the power rule in the previous section and verify it in two special cases: r = −1 and r = .