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NDA 2024 Maths · Mathematics · Derivatives · medium

The derivative of log 10x with respect to x for x>0 is

Single correct option

The derivative of log⁡10x\log_{10}x with respect to xx for x>0x>0 is
  1. A. 1xln⁡10\dfrac{1}{x\ln10}
  2. B. ln⁡10x\dfrac{\ln10}{x}
  3. C. 1x\dfrac1x
  4. D. 10x\dfrac{10}{x}
Show answer and solution

Answer: (A) 1xln⁡10\dfrac{1}{x\ln10}

Change of base: log⁡10x=ln⁡xln⁡10\log_{10}x=\frac{\ln x}{\ln10}, and ln⁡10\ln10 is a constant, so the derivative is 1xln⁡10\frac{1}{x\ln10}. Trap: 1x\frac1x is the derivative of the natural logarithm only, and multiplying by ln⁡10\ln10 instead of dividing by it gives the second option.
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