Differentiate `sin^(-1)(2a xsqrt(1-a^2x^2))` with respect to `sqrt(1-a^2x^2)` , if `-1/(sqrt(2)) lt ax lt 1/(sqrt(2))` .

Explanation

`{u}=sin ^{-1}(2 a {x} sqrt{1-a^{2} {x}^{2}}) text { and } v=sqrt{1-a^{2} {x}^{2}}`


We need to differentiate u with respect to v that is find `frac{d u}{d v}.`

We have


`u=sin ^{-1}(2 a x sqrt{1-a^{2} x^{2}}) `

`Rightarrow u=sin ^{-1}(2 a x sqrt{1-(a x)^{2}})`


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