(5) $y = 3sec x-sin6x$

Explanation:

Step1: Find derivative of $3\sec x$

The derivative of $\sec x$ is $\sec x\tan x$, so the derivative of $3\sec x$ is $3\sec x\tan x$.

Step2: Find derivative of $\sin 6x$

Using the chain - rule. If $u = 6x$, then $\frac{d}{dx}(\sin 6x)=\frac{d(\sin u)}{du}\cdot\frac{du}{dx}$. Since $\frac{d(\sin u)}{du}=\cos u$ and $\frac{du}{dx}=6$, we have $\frac{d}{dx}(\sin 6x)=6\cos 6x$.

Step3: Find derivative of $y$

By the difference rule of differentiation $\frac{d}{dx}(u - v)=\frac{du}{dx}-\frac{dv}{dx}$, where $u = 3\sec x$ and $v=\sin 6x$. So $\frac{dy}{dx}=3\sec x\tan x-6\cos 6x$.

Answer:

$\frac{dy}{dx}=3\sec x\tan x - 6\cos 6x$