Answer to Question #108356 in Calculus for Nimra

Question

F(x)= Arc sinx² . Arc cosx² + 1/sinx²

Answer 1

$F(x)= arc sinx² . arc cosx² + \frac{1}{sinx²}$

$F'(x)=arc sin(x^2).\frac{-2x}{\sqrt{}1-x^4}+arc cos(x^2)\frac{2x}{\sqrt{}1-x^4}-\frac{2xcos(x^2)}{sin^2(x^2)}$

$g(x)=\frac{1}{sin(x^2)}$

$\frac{d}{dx}g(x)=\frac{d}{du}(\frac{1}{sin(u)})\frac{du}{dx}$

$\frac{d}{dx}g(x)=-cosec(x^2)cot(x^2)2x=\frac{-2xcos(x^2)}{sin^2(x^2)}$