Differentiate the following function with respect to `x :` `tan^(-1){x/(sqrt(a^2-x^2))}`,`-a lt xlt a`

Explanation

Y=`tan^(-1){x/(sqrt(a^2-x^2))}`

Let`x=asinθ `

=`theta=sin^(-1)(x/a)`

Y=`tan^(-1){asinθ/(sqrt(a^2-asinθ^2))}`

=`tan^(-1)(asintheta/acostheta)`

Y=`theta=sin^(-1)(x/a)`

differentiate with respect to x

`dy/dx=d/dx(sin^(-1)(x/a))`

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