If $ y=sinx+e^x$, then $\frac{d^2x}{dy^2}$ is equal to :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{sin\, x-e^x}{(cos\, x +e^x)^3}$
$y=\sin x+e^x$
so $\frac{dy}{dx}=\cos x+e^x⇒\frac{dx}{dy}=\frac{1}{\cos x+e^x}$
$⇒\frac{d^2x}{dy^2}=\frac{-1(-\sin x+e^x)}{(\cos x+e^x)^2}\frac{dx}{dy}$
$=\frac{\sin x-e^x}{(\cos x +e^x)^3}$