Differentiate the following function with respect to `x :` `cos^(-1)((1-x^(2n))/(1+x^(2n))) , 0ltxltoo`

Explanation

`y=cos ^{-1}(frac{1-x^{2 n}}{1+x^{2 n}})`

`y=cos ^{-1}(frac{1-(x^{n})^{2}}{1+(x^{n})^{2}})`

let `x^{n}=tan theta quad therefore theta=tan ^{-1}(x^{n})`

`y=cos ^{-1}(frac{1-tan ^{2} theta}{1+tan ^{2} theta})=cos ^{-1}(cos 2 theta)`

`y=2 theta`

Putting the value of theta

`y=2 tan ^{-1}(x^{n})`

differentiate with respect to x

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