# How do you differentiate f(x)=sqrt(cos^3(3x-2)) using the chain rule?

Nov 2, 2016

The answer is =(-9sin(3x-2)cos^2(3x-2))/(2sqrt(cos^3(3x-2)
The derivative of $\left(\sqrt{x}\right) ' = \frac{1}{2 \sqrt{x}}$
and the derivative os $\left(\cos x\right) ' = - \sin x$
As $f \left(x\right) = \sqrt{{\cos}^{3} \left(3 x - 2\right)}$
$f ' \left(x\right) = \frac{1}{2 \sqrt{{\cos}^{3} \left(3 x - 2\right)}}$*$\left(3 {\cos}^{2} \left(3 x - 2\right)\right)$$\left(- \sin \left(3 x - 2\right)\right) \cdot 3$