Find the derivative of the function using the definition of derivative. g(t) = 7t

Solution:

Given, g(t) = 7t

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’(t) = [7(t + h) - (7t)]/h

By further simplification

g’(t) = [7t + 7h - 7t]/h

So we get

g’(t) = [7h]/h

g’(t) = 7

Therefore, g’(t) = 7.

Find the derivative of the function using the definition of derivative. g(t) = 7t

Summary:

The derivative of the function  g(t) = 7t  using the definition of derivative is 7.