Question

If \( y = e^x \), then \( \frac{d^2y}{dx^2} \) is:

• A. \( e^x \)
• B. \( e^{2x} \)
• C. \( e^{x/2} \)
• D. None of these

Hint:

The derivative of \( e^x \) with respect to \( x \) is always \( e^x \), and the second derivative is the same.

Answer 1

The Correct Option is A

Step 1: Differentiating the function.
We are given that \( y = e^x \). The first derivative is: \[ \frac{dy}{dx} = e^x \] Step 2: Finding the second derivative.
Differentiating again, we get: \[ \frac{d^2y}{dx^2} = e^x \] Step 3: Conclusion.
Thus, the second derivative of \( y = e^x \) is \( e^x \), corresponding to option (a).