Question

Find \( \frac{d}{dx} \left(e^{3-2x}\right) \).

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

Hint:

Remember to apply the chain rule when differentiating composite functions, especially when the exponent involves a linear function.

Answer 1

The Correct Option is C

We are asked to differentiate \( e^{3-2x} \). Using the chain rule for differentiation, where the derivative of \( e^u \) with respect to \( x \) is \( e^u \cdot \frac{du}{dx} \), we have: \[ \frac{d}{dx}\left(e^{3-2x}\right) = e^{3-2x} \cdot \frac{d}{dx}(3-2x). \] The derivative of \( 3 - 2x \) with respect to \( x \) is \( -2 \), so the final result is: \[ \frac{d}{dx} \left(e^{3-2x}\right) = -2e^{3-2x}. \] Thus, the correct answer is option (C).