Question

Differentiate the functions with respect to x.
\(2\sqrt{cot\ (x^2)}\)

Answer 1

\(\frac{d}{dx}\)\([2\sqrt{cot\ (x^2)}]\) = 2.\(\frac {1}{2\sqrt {cot\ (x^2)}}\) . \(\frac{d}{dx}\)[cot(x²)]
                            = \(\sqrt {\frac {sin\ (x^2)}{cos\ (x^2)}}\) .- cosec²(x²) . \(\frac {d}{dx}\)(x²)
                            = -\(\sqrt {\frac {sin\ (x^2)}{cos\ (x^2)}}\) . \(\frac {1}{sin^2(x^2)}\) . (2x)
                            = \(\frac {-2x}{\sqrt {cos\ x^2}.\sqrt {sin\ x^2}.sin \ x^2}\)
                            =-\(\frac {-2\sqrt 2x}{\sqrt {cos\ x^2.sin\ x^2}.sin \ x^2}\)
                            =\(\frac {-2\sqrt 2x}{sin\ x^2.\sqrt {sin\ 2x^2}}\)