# Calc2.35

Find the derivative of $f(x)\,$ with respect to $x\,$: $f(x)=\left(\frac{5x}{7x+9}\right)^3\,$

This is a generalized power rule, but the inside function is a quotient.

 $f'(x)\,$ $=3\left(\frac{5x}{7x+9}\right)^2\frac{d\left(\frac{5x}{7x+9}\right)}{dx}\,$ $=3\left(\frac{5x}{7x+9}\right)^2\frac{(7x+9)(5)-(5x)(7)}{(7x+9)^2}\,$ $=3\left(\frac{5x}{7x+9}\right)^2\frac{45}{(7x+9)^2}\,$ $=\frac{3375x^2}{(7x+9)^4}\,$

##### Toolbox

 Get A Wifi Network Switcher Widget for Android