# How do you find the derivative using limits of #f(x)=1-x^2#?

##### 1 Answer

#### Explanation:

In order to find a derivative with limits you need the definition.

Basically the derivative of a function is the limit of the change of the function, as that change approaches 0. This is one reason why derivatives are used for things like "instantaneous rate of change."

In this case

and

so by using FOIL we get

then

So, we can plug this in

Since

Then we group like terms

Then the h terms cancel

This type of algebraic manipulation is very common when using the limit definition for derivation.

Since the limit of a sum is the sum of limits.