Find the derivative of the function using the definition of the derivative. g(x) = 8 − x. 

We will use the concept of differentiation by the first principle and find the derivative.

Answer: The derivative of the function g(x) = 8 − x, using the definition of the derivative is g'(x) = -1.

Let us solve this step by step.

Explanation:

Differentiation by the first principle is stated as

f'(x) = Lim h→0 {[f (x + h) + f (x)] / h} where h << 0

Hence, let us find derivative for g(x)

g'(x) = Lim h→0 {[8 - (x + h) - 8 + x] / h}

g'(x) = -h / h

g'(x) = -1 

Thus, the derivative of the function g(x) = 8 − x, using the definition of the derivative is g'(x) = -1.