Question

y=e^√cotx find dy/dx

Answer 1

here is the answer..........

Answer 2

Answer:

$\frac{d {e}^{ \sqrt{cot \: x} } }{dx} = \frac{ - {cosec}^{2}x \: . {e}^{ \sqrt{cot \: x} } }{2 \sqrt{cot \: x} }$

Step-by-step explanation:

We know that

$\frac{d[ {e}^{f(x)}] }{dx} = {e}^{f(x)} \frac{df(x)}{dx}$

So

$y = {e}^{ \sqrt{cot \: x} } \\ \\ \frac{dy}{dx} = \frac{d{e}^{ \sqrt{cot \: x} }}{dx} \\ \\ = {e}^{ \sqrt{cot \: x} } \frac{d( \sqrt{cot \: x} )}{dx} \\ \\ = {e}^{ \sqrt{cot \: x} } \frac{1}{2 \sqrt{cot \: x} } \frac{d(cot \: x)}{dx} \\ \\ = {e}^{ \sqrt{cot \: x} } \frac{1}{2 \sqrt{cot \: x} } ( - {cosec}^{2} x) \\ \\ \frac{d {e}^{ \sqrt{cot \: x} } }{dx} = \frac{ - {cosec}^{2}x \: . {e}^{ \sqrt{cot \: x} } }{2 \sqrt{cot \: x} }$

Hope it helps you.