What is the derivative of tan^-1 x with respect to cot^-1 x ?

Question

Question

This question was previously asked in

NDA (Held On: 6 Sep 2020) Maths Previous Year paper

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Answer 1

Concept:

Steps for derivatives of functions expressed in the parametric form:

First of all, we write the given functions u and v in terms of the parameter x.
Using differentiation find out du/dx and dv/dx.
Then by using the formula used for solving functions in parametric form i.e.
Lastly substituting the values of du/dx and dv/dx and simplify to obtain the result.

Calculation:

Let u = tan-1 x and v = cot-1 x

Differentiating with respect to x, we get

Now,