# Math Help - inversetrig.2

1. ## inversetrig.2

differentiate f(x) =tan-1(sinx) and f(x) =cos-1(1-x^s)/(1+x^2), stating domain.

thankyou for any help given =)

2. Originally Posted by iiharthero
differentiate f(x) =tan-1(sinx) and f(x) =cos-1(1-x^s)/(1+x^2), stating domain.

thankyou for any help given =)
Using the chain rule and the rule for the derivative of inverse functions:

$\frac{d}{dx}\arctan (\sin x)=\frac{\cos x}{1+\sin^2x}\,,\,\,\forall\,x\in \mathbb{R}$

$\frac{d}{dx}\arccos \left(\frac{1-x^2}{1+x^2}\right)=-\frac{-4x}{(1+x^2)^2}\frac{1}{\sqrt{1-\frac{(1-x^2)^2}{(1+x^2)^2}}}=\frac{4}{1+x^2}\frac{1}{\sqrt {4x^2}}=\frac{2x}{(1+x^2)|x|}$ $\,,\,\,\forall\,x\in \mathbb{R}$