tan^(-1)((6x)/(1-8x^(2)))

If y=tan^(-1)((4x)/(1-5x^(2)))+tan^(-1)((3+8x)/(8-3x)) , then (dy)/(dx) is :

(d)/(dx)[tan^(-1)((6x)/(1+7x^(2)))]+(d)/(dx)[tan^(-1)((5+2x)/(2-5x))]=

Given that , tan^(-1) ((2x)/(1-x^(2))) = {{:(2 tan^(-1) x"," |x| le 1),(-pi +2 tan^(-1)x","x gt 1),(pi+2 tan^(-1)x"," x lt -1):} sin^(-1)((2x)/(1+x^(2))) ={{:(2 tan^(-1)x","|x|le1),(pi -2 tan^(-1)x","x gt 1 and ),(-(pi+2tan^(-1))","x lt -1):} sin^(-1) x + cos^(-1) x = pi//2 " for " - 1 le x le 1 If cos^(-1). (6x)/(1 + 9x^(2)) = - pi/2 + 2 tan^(-1) 3x" , then " x in

tan^(-1)((6x)/(1+16x^(2)))

tan^(-1)((8x)/(1 - 16x^(2)))

Differentiate tan ^(-1) ((8x)/(1-15x^(2))) w.r.to tan ^(-1) ((2xsqrt(1-x^(2)))/(1-2x^(2)))

Differentiate tan ^(-1) ((8x)/(1-15x^(2))) w.r.to x