Question

Differentiate the following questions w.r.t. x.

$e^{si{n}^{-1}x}.$

Answer 1

Let y =$e^{si{n}^{-1}x}$

Differentiate both sides w.r.t. x, we get

$\Rightarrow \frac{dy}{dx}=\frac{d}{dx}\left(e^{si{n}^{-1}x}\right)=e^{si{n}^{-1}x}\frac{d}{dx}si{n}^{-1}x$

$(Usingchainrule\frac{d}{dx}{e}^{ax}=e^{ax}\frac{d}{dx}(ax\left)\right)$

= $e^{si{n}^{-1}x}\frac{1}{\sqrt{1-x^2}}=\frac{e^{si{n}^{-1}x}}{\sqrt{1-x^2}},xϵ(-1,1)$

$[\because \frac{1}{\sqrt{1-x^2}}isdefinedforxϵ(-1,1\left)\right]$