Differentiate `cos^(-1){x/(sqrt(x^2+a^2))}` with respect to `x`

Explanation

Solution:

`y=\sin ^{-1}(2 x^{2}-1)`

`\sin y=2 x^{2}-1`

`\frac{d}{d x}(\sin y)=\frac{d}{d x}(2 x^{2}-1)`

`\cos y \cdot \frac{d y}{d x}=4 x`

`\frac{d y}{d x}=\frac{4 x}{\cos y}`

`\because, \sin y=2 x^{2}-1`

`\cos y=\sqrt{1-(2 x^{2}-1)^{2}}`

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