Find each derivative g) \( y=\frac{e^{x}}{1+\sin x} \)

To find the derivative of the function \( y = \frac{e^x}{1 + \sin x} \), we can use the quotient rule, which states that if you have a function \( y = \frac{u}{v} \), then the derivative \( y' \) is given by \( y' = \frac{u'v - uv'}{v^2} \). Here, \( u = e^x \) and \( v = 1 + \sin x \). - The derivative of \( u \) is \( u' = e^x \). - The derivative of \( v \) is \( v' = \cos x \). Now applying the quotient rule: \[ y' = \frac{e^x(1 + \sin x) - e^x(\cos x)}{(1 + \sin x)^2} \] This simplifies to: \[ y' = \frac{e^x(1 + \sin x - \cos x)}{(1 + \sin x)^2} \] Thus, the derivative \( y' \) is: \[ y' = \frac{e^x(1 + \sin x - \cos x)}{(1 + \sin x)^2} \]