tan^(-1)(sqrt(a)-sqrt(x))/(1+sqrt(ax))

Find the (dy)/(dx) of y=tan^(-1)((sqrt(a)-sqrt(x))/(1+sqrt(a x)))

Differentiate tan^(-1)[(sqrt(x)+sqrt(a))/(1-sqrt(ax))] w.r.t. x.

y = tan^(-1)((sqrt(x)+sqrt(a))/(1-sqrt(ax))), find dy/dx.

Prove that: i) tan^(-1)(sqrt(x)+sqrt(y))/(1-sqrt(xy))=tan^(-1)sqrt(x)+tan^(-1)sqrt(y) ii) tan^(-1)(x+sqrt(x))/(1-x^(3//2))=tan^(-1)x+tan^(-1)sqrt(x) iii) tan^(-1)(sinx)/(1+cosx)=x/2

If tan^(-1) sqrt((1-sqrt(x))/(1+sqrt(x))) = (pi)/(4)-(alpha)/(2) , then express tan^(2)alpha in terms of x.

int(sqrt(a)-sqrt(x))/(1-sqrt(ax))dx

Differentiate tan^(-1)((sqrt(x)+sqrt(a))/(1-sqrt(xa))) with respect to x

The differential coefficient of tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))

The differential coefficient of tan^(- 1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))