Answer
$f'(x)=-\frac{3\sin\left(\frac{x}{x+1}\right)\cos^2\left(\frac{x}{x+1}\right)}{{(x+1)^2}}$
Work Step by Step
$f(x)=cos^3(\frac{x}{x+1})$
$f'(x)=3cos^2(\frac{x}{x+1})\times\frac{dy}{dx}cos(\frac{x}{x+1})$
$f'(x)=3cos^2(\frac{x}{x+1})\times{-sin(\frac{x}{x+1})}\times\frac{1\times{x+1}-(x\times1)}{(x+1)^2}$
$f'(x)=3cos^2(\frac{x}{x+1})\times{-sin(\frac{x}{x+1})}\times\frac{{x+1}-x}{(x+1)^2}$
$f'(x)=3cos^2(\frac{x}{x+1})\times{-sin(\frac{x}{x+1})}\times\frac{1}{(x+1)^2}$
$f'(x)=-\frac{3\sin\left(\frac{x}{x+1}\right)\cos^2\left(\frac{x}{x+1}\right)}{{(x+1)^2}}$
