Differentiation Of Trigonometric Functions

$\sec x \tan x$

The derivative of $\sec x$ is $\sec x \tan x$, derived using the quotient rule or chain rule.

$-\csc x \cot x$

The derivative of $\csc x$ is $-\csc x \cot x$, derived using the quotient rule or first principle.

$2 \cos 2x$

Using chain rule, $\frac{d}{dx}(\sin 2x) = \cos 2x \cdot 2 = 2 \cos 2x$.

$-3 \sin 3x$

Using chain rule, $\frac{d}{dx}(\cos 3x) = -\sin 3x \cdot 3 = -3 \sin 3x$.