Question

How do you find the derivative of `f(x)=((18x)/(4+(x^2)))`?

Answer 1

When you have a function in the form `f(x)=(p(x))/(q(x))` using the quotient rule for the derivative you get

`f'(x)=(p'(x)*q(x)-p(x)*q'(x))/(q(x)^2)`

hence for `p(x)=18x` and `q(x)=4+x^2`

you get

`f'(x)=-18*(x^2-4)/(x^2+4)^2`