Question

For the following exercises, use the definition of derivative to calculate the derivative of each function.

f(x) = 5π

Answer 1

For any function f(x), its derivative f\'(x) is given by the formula:

f\'(x) = limh→0{f(x + h) – f(x)/h}

 

Now consider the following function:

f(x) = 5π

 

Calculate derivative f\'(x) is as follows:

limh→0{f(x + h) – f(x)/h} = limh→0{(5π – 5π)/h}

                                           = limh→0(0/h)

                                           = limh→0(0)

                                            = 0