Using the limit definition, how do you find the derivative of #1/(x^2-1)#?
Please refer to explanation below for more information.
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
Then, we can directly substitute
#f'(x) = (-2x)/((x^2-1)(x^2-1)) = (-2x)/(x^2-1)^2#