Question

\(\frac{d}{dx}[\ln(2x)]\) is equal to

• A. \(\frac{1}{2x}\)
• B. \(\frac{1}{x}\)
• C. \(\frac{1}{2}\)
• D. \(x\)

Hint:

Always simplify logarithmic expressions using log rules before differentiating.

Answer 1

The Correct Option is B

We use the logarithmic identity:
\(\ln(2x) = \ln 2 + \ln x\).

Step 1: Differentiate both sides.
Derivative of \(\ln 2\) is 0 (constant).
Derivative of \(\ln x\) is \(\frac{1}{x}\).

Step 2: Final result.
\(\frac{d}{dx}[\ln(2x)] = \frac{1}{x}\).