Question

dy/dx,if y = ex/sinx

Answer 1

Solution:-

y = e^x /sinx

diff .with r to x.

dy/dx = (sinx .e^x - e^x .cosx)/ sin^2x

= e^x(sinx -cosx)/sin^2x

Answer 2

$\frac{dy}{dx} = \frac{d}{dx} ( \frac{ {e}^{x} }{sinx} )$
$\frac{dy}{dx} = \frac{ \sin(x) \frac{d}{dx} {e}^{x} - {e}^{x} \frac{d}{dx} \sin(x) }{ { \sin }^{2}(x) }$
$\frac{dy}{dx } = \frac{ \sin(x). {e}^{x} - {e}^{x}. \cos(x) }{ { \sin }^{2}(x) }$
$\frac{dy}{dx} = \frac{ {e}^{x}( \sin(x) - \cos(x) )}{ { \sin }^{2}(x) }$