Question

The function whose derivative is equal to itself is

• A. \(\sin x\)
• B. \(\cos x\)
• C. \(\log x\)
• D. \(e^x\)

Hint:

\(e^x\) is the only function whose rate of change equals its value.

Answer 1

The Correct Option is D

Concept: A function equals its derivative if \(\frac{d}{dx}f(x) = f(x)\).

Step 1: Check each option. \[ \frac{d}{dx}(e^x) = e^x \quad \text{(matches)} \] \[ \frac{d}{dx}(\sin x) = \cos x \neq \sin x \] \[ \frac{d}{dx}(\cos x) = -\sin x \neq \cos x \] \[ \frac{d}{dx}(\log x) = \frac{1}{x} \neq \log x \]

Step 2: Conclusion. Only \(e^x\) remains unchanged after differentiation.