In Exercise, use limits to compute f′(x) [Hint: In Exercise, use the rationalization trick...

In Exercise, use limits to compute f′(x) [Hint: In Exercise, use the rationalization trick of Example.]

f(x) =

Example

Derivative of a Function with a Radical Find the derivative of f(x) = x > 0.

SOLUTION In simplifying the difference quotient, we use the algebraic identity (a + b)(a − b) = a2 − b2. So,

Sometimes, we can use our knowledge of differentiation to evaluate some difficult limits. Here is one illustration.