Differentiate tan^-1(x/√(1 - x^2)) with respect to cos^-1 (2x^2 - 1).

Question

Differentiate tan^-1\(\left(\cfrac{\text x}{\sqrt{1-\text x^2}}\right)\)with respect to cos^-1(2x² - 1).

tan^-1(x/√(1 - x²))

Answer 1

Given : Let u = tan^-1\(\left(\cfrac{\text x}{\sqrt{1-\text x^2}}\right)\)and v = cos^-1(2x² - 1).

tan^-1(x/√(1 - x²))

To differentiate : tan^-1\(\cfrac{\text x}{\sqrt{1-\text x^2}}\) with respect to cos^-1(2x² - 1)

Formula used : 

The CHAIN RULE states that the derivative of f(g(x)) is f’(g(x)).g’(x)

Let u = tan^-1\(\cfrac{\text x}{\sqrt{1-\text x^2}}\) and v = cos^-1(2x² - 1)

Differentiating u with respect to x

Differentiating v with respect to x