Differentiate the following functions with respect to `x :` `tan^(-1)sqrt((a-x)/(a+x)),-altxlta`

Explanation

`f(x)=tan^(-1)(sqrt((a-x)/(a+x)))`

`g(x)=sqrt((a-x)/(a+x))`

`f(x)=tan^(-1)(g(x))`

diff. with respect to x

`f'(x)=1/(1+(g(x))^2)g'(x)`

`=1/(1+((a-x)/(a+x)))g'(x)`

`f'(x)=(a+x)/(a+x+a-x)g'(x)=(a+x)/(2a)g'(x)`

`g(x)=d/dx(sqrt((a-x)/(a+x)))`

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