Differentiate the following function `sin^(-1)(x/(x^2+a^2))`

Explanation

Let `y= sin^(-1)(x/(x^2+a^2))`

On differentiating `y` with respect to `x`, we get


`frac{d y}{d x}=frac{1}{sqrt{1-frac{x^{2}}{x^{2}+a^{2}}}}` `cdot` `frac{{1 cdot sqrt{x^{2}+a^{2}}-frac{x^{2 x}}{x sqrt{x^{2}+a^{2}}}.}}{{x^{2}+a^{2}}]`


We know `(u / v)’=frac{ u’u –v’u}{v^{2}}`


`frac{sqrt{x^{2}}+a^{2}}{a} cdot[frac{x^{2}+a^{2}-x^{2}}{sqrt{x^{2}+a^{2}}(x^{2}+a^{2})}].`