If y = x + e^x , find d^2x/dy^2.

Question

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

Answer 1

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