Question

Find $\frac{dy}{dx}$ if $f\left(x\right)=\cos 3x.6e^{6x}$

Answer 1

$f\left(x\right)=y=\cos 3x.6e^{6x}$

Using product rule and chain rule:

$\frac{dy}{dx}=\cos 3x{.6}^2{e}^{6x}-3\sin 3x.6e^{6x}$

$\frac{dy}{dx}=18e^{6x}[2\cos 3x-\sin 3x]$