Answer
$f'(x)=\frac{-3sin(3\sqrt x)cos(3\sqrt x)}{\sqrt x}$
Work Step by Step
$f(x)=cos^2(3\sqrt x)$
$f(x)=cos^2(3x^{\frac{1}{2}})$
$f'(x)=2cos^{2-1}(3\sqrt x)\times(\frac{d}{dx})(cos(3\sqrt x)))$
$f'(x)=2cos^{2-1}(3\sqrt x)\times(-sin(3\sqrt x))\times(\frac{d}{dx})(3x^{\frac{1}{2}})$
$f'(x)=2cos^1(3\sqrt x)\times(-sin(3\sqrt x))\times(\frac{3}{2}x^{\frac{1}{2}-1})$
$f'(x)=-sin(3\sqrt x)2cos(3\sqrt x)\times(\frac{3}{2}x^{\frac{-1}{2}})$
$f'(x)=\frac{-6sin(3\sqrt x)cos(3\sqrt x)}{2\sqrt x}$
$f'(x)=\frac{-3sin(3\sqrt x)cos(3\sqrt x)}{\sqrt x}$
