Question

whats the differentiate of secxtanx

Answer 1

Two of many ways to do this:
\[\text{straight product rule:}\\
\frac{d}{dx}\sec x\tan x=\left(\frac{d}{dx}\sec x\right)\tan x+\sec x\left(\frac{d}{dx}\tan x\right)\]
\[\text{identity manipulation, then quotient/power/chain rules:}\\
\sec x\tan x=\frac{1}{\cos x}\cdot\frac{\sin x}{\cos x}=\frac{\sin x}{\cos^2x}\\\\
~~\Rightarrow~~\frac{d}{dx}\sec x\tan x=\frac{\cos^2x\left(\dfrac{d}{dx}\sin x\right)-\sin x\left(\dfrac{d}{dx}\cos^2x\right)}{\left(\cos^2x\right)^2}\]