Question

differentiate e√cotx with respect to x​

Answer 1

Answer:

Let y = e^cotx , now differentiating with respect to x and using chain rule , we get ,

dy/dx = d/dx(e^cotx)

=> dy/dx = e^cotx * d/dx(cotx)

=> dy/dx = e^cotx{-cosec^2(x)}

=> dy/dx = - cosec^2(x)*e^cotx

Answer 2

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