Differentiate the following function with respect of `x` : `(e^x)/(1+sinx)`

Explanation

`y={dx}\frac{e^{x}}{ (1+\sin x)}`


Differentiating the function w.r.t. `x` we get:


`=\frac{(1+\sin x) \frac{d}{d x}(e^{x})-e^{x} \frac{d}{d x}(1+\sin x)}{(1+\sin x)^{2}} `


`=\frac{(1+\sin x) e^{x}-e^{x} \cos x}{(1+\sin x)^{2}}`


`=\frac{e^{x}(1+\sin x-\cos x)}{(1+\sin x)^{2}}`