Find the derivative of the function using the definition of derivative. g(x) = 4 - x

Solution:

Differentiation means the rate of change of one quantity with respect to another.

The speed is calculated as the rate of change of distance with respect to time.

Given, g(x) = 4 - x

We have to find the derivative of the function.

The differentiation by the first principle states that,

f’(x) = [f(x + h) - f(x)]/h

Where h << 0

Now, g’(x) = [g(x + h) - g(x)]/h

g’(x) = [4 - (x + h) - (4 - x)]/h

g’(x) = [4 - x - h - 4 + x]/h

g’(x) = [-h]/h

g’(x) = -1

Therefore, g’(x) = -1.

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Find the derivative of the function using the definition of derivative. g(x) = 4 - x

Summary:

The derivative of the function g(x) = 4 - x using the definition of derivative is -1.