Find the derivative of f(x) = 4x + 7 at x = 5.

Solution:

A derivative is the rate of change of a quantity y with respect to another quantity x.

A derivative is also termed the differential coefficient of y with respect to x.

Differentiation is the process of finding the derivative of a function.

The derivative of f(x) is given as

df(x)/dx = d(4x + 7)/dx

f’(x) = df(x)/dx = d(4x)/dx + d(7)/dx

f’(x) = 4dx/dx + d(7)/dx

f’(x) = 4 + 0

f’(x) = 4 is a constant

At x = 5 the derivative of the function f(x) = 4x + 7 at x = 5 is 4

Find the derivative of f(x) = 4x + 7 at x = 5.

Summary:

The derivative of f(x) = 4x + 7 at x = 5 is 4