Question

please give me the answer immediately.

☆Differentiate with respect to x.

1. see the pic and give me answer.

Answer 1

$\bf let\:\: y = 2\sqrt{cotx^{2}} \\ \\ \bf \:\:\: put \:\:\:x^{2} = t\:\:,\:\:y = 2\sqrt{cot(t)} \\ \\ \bf put\:\:\: cot(t) = z \\ \\ \bf y = 2\sqrt{z} \\ \\ \bf using \:\:chain \:\:rule, \:\:dy/dx = dy/dz * dz/dt * dt/dx \\ \\ \bf dy/dx = 2/2\sqrt{z} * (-cosec^{2}t) * 2x \\ \\ \bf dy/dx =2x (-cosec^{2}x^{2})/\sqrt{cotx^{2}} \\ \\ \bf I \:\:HOPE \:\:ITS\:\: HELP \:\:YOU \:\:DEAR, \\ \\ THANKS$

Answer 2

$Given : 2 \sqrt{cot(x^2)}$

$= \ \textgreater \ 2 * \frac{d}{dx} [ \sqrt{cot(x^2)}]$

$= \ \textgreater \ 2 * \frac{1}{2} cot^{ \frac{1}{2} - 1} (x^2) * \frac{d}{dx} [cot(x^2)]$

$= \ \textgreater \ \frac{(-cosec(x^2)) * \frac{d}{dx}[x^2] }{ \sqrt{cot(x^2)} }$

$= \ \textgreater \ - \frac{2xcosec^2(x^2)}{ \sqrt{cot(x^2)} }$



Hope this helps!