tan^(-1)((4sqrt(x))/(1-4x))

Find (dy)/(dx) , when y="tan"^(-1)(sqrt(x)-4sqrt(x))/(1+4sqrt(x^(3)))

Prove that tan^(-1) ((1-sqrt(x))/(1+sqrt(x))) = pi/4 - tan^(-1) sqrt(x) , "where" x gt 0

Prove that tan^(-1)((6x-8x^(3))/(1-12x^(2)))-tan^(-1)((4x)/(1-4x^(2)))= tan^(-1)2x,|2x| lt (1)/(sqrt(3)) .

Differentiate cos^(-1)(4x^(3)-3x) with respect to tan^(-1)((sqrt(1-x^(2)))/(x)), if 1/2

Differentiate tan^(-1)((1+2x)/(1-2x))wdotrdottsqrt(1+4x^2) and tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)(x)

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

Prove That : tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/4-1/2cos^(-1)x =1/(sqrt(2))ltxle1

Prove That : tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/4-1/2cos^(-1)x,-1/(sqrt(2))ltxle1

Prove That : tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/4-1/2cos^(-1)x,-1/(sqrt(2))ltxle1

Prove that : tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=pi/4-1/2cos^(-1)x,-1/sqrt2lexle1