Question

Use the four-step process to find the derivative for:

You need to use:  

Answer 1

Solution :- Given a function f(x), the definition of f'(x), the derivative of f(x),

that is f'(x) = lim h→0 [f (x + h) − f(x)]/ h , provided the limit exists.

The derivative function f '(x) is sometimes also called a slope predictor function.

The following is a four-step process to compute f' (x) by the definition.

Input: a function f(x)

Step 1:- Write f(x + h) and f(x).

Step 2 Compute f(x + h) − f(x). Combine like terms. If h is a common factor of the terms, factor the expression by removing the common factor h.

Step 3 Simply [f(x + h) − f(x)]/ h .

As h → 0 in the last step, we must cancel the zero factor h in the denominator in Step 3.

Step 4 Compute the lim h→0 [f(x + h) − f(x) ]/ h by letting h → 0 in the simplified expression.