Question

1. y = sec x + csc x

Explanation:

Step1: Recall derivative formulas

The derivative of $\sec x$ is $\sec x\tan x$ and the derivative of $\csc x$ is $-\csc x\cot x$.

Step2: Apply sum - rule of differentiation

If $y = u + v$, where $u=\sec x$ and $v = \csc x$, then $y^\prime=u^\prime + v^\prime$.
So $y^\prime=\frac{d}{dx}(\sec x)+\frac{d}{dx}(\csc x)$.
Substituting the derivative formulas, we get $y^\prime=\sec x\tan x-\csc x\cot x$.

Answer:

$y^\prime=\sec x\tan x - \csc x\cot x$