Calc2.35

From Exampleproblems

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.

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