Question

Find the derivative of the function f(x) = sin2(x) + tan2(x).

Answer 1

`f(x)=\sin^2(x)+\tan^2(x)\implies f(x)=[\sin(x)]^2+[\tan(x)]^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{df}{dx}=\stackrel{ \textit{chain rule} }{2[\sin(x)]\cos(x)}~~ + ~~\stackrel{ \textit{chain rule} }{2[\tan(x)]\sec^2(x)} \\\\\\ \cfrac{df}{dx}=2\sin(x)\cos(x)~~ + ~~2\tan(x)\sec^2(x)`