Question

F(x)= Arc cotx² + Arc sinx² . x²

Answer 1

$F(x)=Arccot(x^2)+x^2Arcsin(x^2)$

$\frac{dF}{dx}=-\frac{1}{1+(x^2)^2}\frac{d}{dx}(x^2)+2xArcsin(x^2)+\frac{x^2}{\sqrt{1-(x^2)^2}}\frac{d}{dx}(x^2)=$

$=-\frac{2x}{1+(x^2)^2}+2xArcsin(x^2)+\frac{2x^3}{\sqrt{1-(x^2)^2}}$