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

When you have a function in the form $f \left(x\right) = \frac{p \left(x\right)}{q \left(x\right)}$ using the quotient rule for the derivative you get
$f ' \left(x\right) = \frac{p ' \left(x\right) \cdot q \left(x\right) - p \left(x\right) \cdot q ' \left(x\right)}{q {\left(x\right)}^{2}}$
hence for $p \left(x\right) = 18 x$ and $q \left(x\right) = 4 + {x}^{2}$
$f ' \left(x\right) = - 18 \cdot \frac{{x}^{2} - 4}{{x}^{2} + 4} ^ 2$