Question

How do you find the derivative of the function using the definition of derivative `f(x) = 10`?

Answer 1

`f'(x) =0`

Explanation:

The derivative of a function is a measure of the rate of change of the function.

In this case the function is not changing as10 is a constant.

if f(x) = c where c is a constant then f'(x) = 0 The derivative of a constant is always zero.

EDIT: Definition added

Limit definition

The definition of the derivative:

`(df(x))/dx=lim_(h->0)(f(x+h)-f(x))/h`

Note: Since there is no `x` to substitute for `x+h`, no difference is noticed:

`lim_(h->0)(f(x+h)-f(x))/h=lim_(h->0)(10-10)/h=lim_(h->0)(0/h)=0`

So the derivative is equal to zero.