Question:
\(\frac{d}{dx}[\ln(2x)]\) is equal to
\(\frac{d}{dx}[\ln(2x)]\) is equal to
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Always simplify logarithmic expressions using log rules before differentiating.
Updated On: Jan 2, 2026
- \(\frac{1}{2x}\)
- \(\frac{1}{x}\)
- \(\frac{1}{2}\)
- \(x\)
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The Correct Option is B
Solution and Explanation
We use the logarithmic identity:
\(\ln(2x) = \ln 2 + \ln x\).
\(\ln(2x) = \ln 2 + \ln x\).
Step 1: Differentiate both sides.
Derivative of \(\ln 2\) is 0 (constant).
Derivative of \(\ln x\) is \(\frac{1}{x}\).
Step 2: Final result.
\(\frac{d}{dx}[\ln(2x)] = \frac{1}{x}\).
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