Find the derivative of the function using the definition of derivative. g(x) = 5 - x

Solution:

Given, g(x) = 5 - x

We have to find the derivative of the function.

Derivative by the first principle is stated as

f’(x) = [f(x + h) - f(x)] / h where h << 0

So, g’(x) = [5 - (x + h) - (5 - x) ] /h

g’(x) = [5 - x - h - 5 + x] / h

g’(x) = [5 - 5 - x + x - h] / h

g’(x) = (-h)/h

g’(x) = -1

Therefore, the derivative of the function is g’(x) = -1.

Find the derivative of the function using the definition of derivative. g(x) = 5 - x

Summary:

The derivative of the function g(x) = 5 - x using the definition of derivative is g’(x) = -1.