Find the derivative of the function using the definition of derivative. g(x) = 1 - x

Solution:

It is given that

g(x) = 1 - x

The first principle derivative states that.

f' (x) = [f(x + h) - f(x)] / h where h is very very less than 0.

In terms of g(x) we have,

g' (x) = [g(x + h) - g(x)] / h where h << 0.

Substituting the values

g' (x) = [1 - (x + h) - 1 + x] / h

g' (x) = -h / h = -1

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

Find the derivative of the function using the definition of derivative. g(x) = 1 - x

Summary:

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