# How do you differentiate #f(x)=((18x)/(4+x^2))# using the quotient rule?

##### 1 Answer

Oct 31, 2015

The derivative is

#### Explanation:

The quotient rule states that

Let's calculate all the quantities we need:

- Since
#f(x)=18x# , we have that#f'(x)=18# . - Since
#g(x) = 4+x^2# , we have that#g'(x)=2x# . - As for
#g(x)# , we'll just write#(4+x^2)^2# .

So, if we substitute all these functions in

we can easily expand the numerator into

So, the expression becomes