if $f(x)=cos x - 5\tan x$, then $f(x)=$

Explanation:

Step1: Recall derivative rules

The derivative of $\cos x$ is $-\sin x$ and the derivative of $\tan x$ is $\sec^{2}x$. Also, use the constant - multiple rule: if $y = cf(x)$, then $y'=cf'(x)$.

Step2: Differentiate term - by - term

For $y = \cos x-5\tan x$, the derivative of $\cos x$ is $-\sin x$ and the derivative of $- 5\tan x$ is $-5\sec^{2}x$ (by the constant - multiple rule with $c = - 5$ and the derivative of $\tan x$ being $\sec^{2}x$). So $f'(x)=-\sin x - 5\sec^{2}x$.

Answer:

$-\sin x - 5\sec^{2}x$