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A day full of math games & activities. Find one near you.
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.
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