Differentiate the following function with respect to `x :` `sin^(-1)(x/(sqrt(a^2+x^2)))`

Explanation

`y=sin ^{-1}{frac{x}{sqrt{x^{2}+a^{2}}}}`

Let `x=a tan theta`

`y=sin ^{-1}{frac{{atan} theta}{sqrt{a^{2} tan ^{2} theta+a^{2}}}} `

Using `1+tan ^{2} theta=sec ^{2} theta `

`y=sin ^{-1}{frac{{atan} theta}{a sqrt{tan ^{2} theta+1}}} `

`y=sin ^{-1}{frac{{atan} theta}{a sqrt{sec ^{2} theta}}} `

`y=sin ^{-1}{frac{tan theta}{sec theta}} `

`y=sin ^{-1}(sin theta) `

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