Using derivative prove: `tan^-1x + cot^-1 x= pi/2`

Using derivative, prove tan^(-1) x + cot^(-1) x = frac{pi}{2}

Using derivative prove: sec^-1 x + cosec^-1 x=pi/2 , for |x|ge1 .

Using derivative prove that sin^(-1) x + cos^(-1) x = (pi)/2

Using derivative, prove sec^(-1) x + cosec^(-1) x = frac{pi}{2}

Select the correct option from the given alternatives: The value of cot(tan^-1 2x+cot^-1 2x) is A) 0 B) 2x C) pi+2x D) pi-2x

The derivative of tan^(-1)((sqrt(1+x^2)-1)/x) with respect to tan^(-1)((2xsqrt(1-x^2))/(1-2x^2)) at x=0 is

What is the derivative of tan^(-1)((sqrtx-x)/(1+x^(3//2))) at x = 1?

The derivative of f(x)=x^(tan^-1 x) with respect to g(x)=sec^-1(1/(2x^2-1)) is