Question

\(\dfrac{d}{dx}\big(\log_{e}(10x)\big)=\) ?

• A. \(\dfrac{1}{10x}\)
• B. \(\dfrac{10}{x}\)
• C. \(10x\)
• D. \(\dfrac{1}{x}\)

Hint:

$\dfrac{d}{dx}\ln(ax)=\dfrac{1}{x}$ for any constant \(a>0\).

Answer 1

The Correct Option is D

\(\ln(10x)=\ln10+\ln x\). Constant's derivative is \(0\). \(\dfrac{d}{dx}(\ln x)=\dfrac{1}{x}\). Hence the result is \(1/x\).