Question

y = \frac{e^{x}}{sin x} dy/dx ज्ञात कीजिए

Answer 1

dy/dx   =eˣ (Sinx - Cosx) /Sin²x  यदि y  =  eˣ/Sinx

Step-by-step explanation:

y  =  eˣ/Sinx

dy/dx   =    (eˣ)'/Sinx   + eˣ * (1/Sinx)'

=> dy/dx   =  eˣ/Sinx   + eˣ ( - 1/Sin²x) (Cosx)

=> dy/dx   =eˣ /Sinx  -   eˣCosx/Sin²x

=> dy/dx   =eˣ Sinx/Sin²x  -   eˣCosx/Sin²x

=> dy/dx   =eˣ (Sinx - Cosx) /Sin²x

और अधिक जानें :

sin(x²+5)"

brainly.in/question/15286193

sin (ax+b) फलन का अवकलन कीजिए

brainly.in/question/15286166

Answer 2

Question :-

$\rm \: if \: y \: = \frac{ {e}^{x} }{ \sin x} \: \: then \: find \: \frac{dy}{dx}$

Answer :-

$\to \boxed{ \rm \frac{dy}{dx} = \frac{ {e}^{x} ( \sin x - \cos x)}{ { \sin}^{2} x} } \:$

To Find :-

$\to \rm \: \frac{dy}{dx}$

Concept used :-

If two functions of x is in fraction then we have to use quotient rule of differentiation that is -

$\rm \to \: \frac{d}{dx} \frac{u}{v} \: = \frac{v \frac{d}{dx} u - u \frac{d}{dx} v}{ {v}^{2} }$

Solution :-

We have

$\to \rm \: y = \frac{ {e}^{x} }{ \sin x} \\ \\ \sf differentiate \: with \: respect \: to \: x \\ \\ \to \rm \frac{dy}{dx} \: = \frac{ \sin x \frac{d}{dx} {e}^{x} - {e}^{x} \frac{d}{dx} \sin x}{ { \sin}^{2}x } \\ \\ \boxed{ \because \rm \frac{d}{dx} {e}^{x} = {e}^{x} \: \: \: and \: \: y \: \frac{d}{dx} \sin x = \cos x } \\ \therefore \: \\ \\ \to \rm \frac{dy}{dx} = \frac{ {e}^{x} \sin x - \cos x \: {e}^{x} }{ { \sin}^{2} x} \\ \sf or \\ \\ \to \boxed{ \rm \frac{dy}{dx} = \frac{ {e}^{x} ( \sin x - \cos x)}{ { \sin}^{2} x} }$