If y = x + ex , find \(\frac{d^2x}{dy^2}.\)

1.	If y = x + ex , find \(\frac{d^2x}{dy^2}.\)
Answer» Given: \(y=x+e^x\) \(\frac{d^2x}{d^2y}=\frac{1}{\frac{d^2y}{dx^2}}\) \(\frac{dy}{dx}=1+e^x\) \(\frac{d^2y}{dx^2}=e^x\) \(\frac{d^2x}{d^2y}=\frac{1}{e^x}\) =e^-x

Answer»

Given:

\(y=x+e^x\)

\(\frac{d^2x}{d^2y}=\frac{1}{\frac{d^2y}{dx^2}}\)

\(\frac{dy}{dx}=1+e^x\)

\(\frac{d^2y}{dx^2}=e^x\)

\(\frac{d^2x}{d^2y}=\frac{1}{e^x}\)

=e^-x

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