# Using the limit definition, how do you find the derivative of #1/(x^2-1)#?

##### 1 Answer

Please refer to explanation below for more information.

#### Explanation:

If you apply limit to a difference quotient formula, you will get the derivative of the function using the limit of definition

**Remember:** The difference quotient formula is

Here is how:

**Step 1**: Let's set it up, with the given function

**Step 2:** We know,

**Step 3**: Let's set up the limit, to find the derivative

**Step 4**: Let's simplify the expression first before we evaluate the limit (here comes the ALGEBRA!!)

Find the

least common denominator

Multiply the numerator and distribute negative one and divide the fraction to get

Simply, by combine all the like terms, and factor out the common factor on the numerator to get

Remember,

Then, we can directly substitute

#lim_(h->0) (-2x-0)/((x^2-1)[(x+0)^2-1])#

#f'(x) = (-2x)/((x^2-1)(x^2-1)) = (-2x)/(x^2-1)^2#