Question

If \( y = \sqrt{e^x} \), \( x > 0 \), then \( \frac{dy}{dx} = \underline{\hspace{2cm}} \)

Hint:

When differentiating exponential functions, use the chain rule for handling expressions in the exponent.

Answer 1

Step 1: Differentiate \( y = \sqrt{e^x} \).
We can rewrite \( y = e^{x/2} \). Differentiating with respect to \( x \), we get: \[ \frac{dy}{dx} = \frac{1}{2} e^{x/2}. \]

Step 2: Conclusion.
Thus, \( \frac{dy}{dx} = \frac{1}{2} e^{x/2} \).