Question

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

• A. \( e^x \)
• B. \( -\frac{e^x}{(1+e^x)^2} \)
• C. \( -\frac{e^x}{(1+e^x)^3} \)
• D. \( \frac{e^x}{(1+e^x)^3} \)

Hint:

For inverse differentiation, use \( \frac{dx}{dy}=\frac{1}{dy/dx} \) and then apply chain rule carefully for second derivative.

Answer 1

The Correct Option is C