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)
= $\frac {-2x}{\sqrt {cos\ x^2}.\sqrt {sin\ x^2}.sin \ x^2}$
=-$\frac {-2\sqrt 2x}{\sqrt {cos\ x^2.sin\ x^2}.sin \ x^2}$
=$\frac {-2\sqrt 2x}{sin\ x^2.\sqrt {sin\ 2x^2}}$