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

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

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

If f(x) =tan^(-1)((x)/(1+20x^(2))) , show that, f'(x)=(5)/(1+25x^(2))-(4)/(1+16x^(2))

Integrate the following respect to x. (i) (xsin^(-1)x)/(sqrt(1-x^2)) (ii) x^5e^(x^2) (iii) tan^(-1)((8x)/(1-16x^2)) (iv) sin^(-1)((2x)/(1+x^2))

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

(d)/(dx)[tan^(-1)((10x)/(4-6x^(2)))]=

tan^-1((5x)/(1-6x^2))

tan^-1((5x)/(1-6x^2))

If y = tan ^(-1) ((2x )/( 1 -x ^(2))) + tan ^(-1) ((3x - x ^(3))/( 1 - 3x ^(2)))- tan ^(-1) ((4x - 4x ^(3))/( 1 - 6x + x ^(4))), then show that (dy)/(dx) = (1)/(1 + x ^(2)).

Differentiate tan^(-1){(5x)/(1-6x^(2))}-(1)/(sqrt(6))