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.
Differentiation by the first principle is stated as
f'(x) = [f (x + h) + f (x)] / h where h << 0
Hence, let us find derivative for g(x)
g'(x) = [8 - (x + h) - 8 + x] / h
g'(x) = -h / h
g'(x) = -1