Find `d/(dx)cot^(-1) tan(pi/2-x)`.

Find (dy)/(dx) when y=cot^-1tan(pi/2-x)

Find d/(dx) In sin^(-1)cos((pi-2e^x)/2) .

Find d/dx(sin^(-1)x)^(x^2)

If A=(1)/(pi)[{:(sin^(-1)(pix),tan^(-1)(x//pi)),(sin^(-1)(x//pi),cot^(-1)(pix)):}] and B=(1)/(pi)[{:(-cos^(-1)(pix),tan^(-1)(x//pi)),(sin^(-1)(pi//x),-tan^(-1)(pix)):}] then find (A-B)

If y=sec^(-1)((x^(2)+1)/(x^(2)-1)) , then find (dy)/(dx) . Here f^(-1)(x) expression is of the form (x^(2)+a^(2))/(x^(2)-a^(2)) , so we substitute x=tan theta and then use suitable trigonometrical formula to write it in simplest form and then differentiate

If "tan"^(-1)x+"tan"^(-1)y=(4pi)/(5) , then find "cot"^(-1)x+"cot"^(-1)y .

If tan^(-1)(sqrt(3)) +cot^(-1)x =(pi)/(2) , then find the value of x.

If tan^(-1)x +tan^(-1) y +tan^(-1) z=pi/2 . Show that xy+yz+zx =1.

Prove statement "cot"^(-1)("tan"2x) +"cot"^(-1)(-"tan"2x) = pi