Question

Find the derivative of \[ \frac{d}{dx} \left( \log x^{100} \right). \]

• A. \( \frac{1}{x^{100}} \)
• B. \( \frac{1}{x} \)
• C. \( \frac{100}{x} \)
• D. \( \frac{1}{100x} \)

Hint:

For logarithmic functions with exponents, bring the exponent down as a coefficient before differentiating.

Answer 1

The Correct Option is C

We are asked to differentiate \( \log x^{100} \). Using the logarithmic property \( \log a^b = b \log a \), we can rewrite the expression as: \[ \log x^{100} = 100 \log x. \] Now, differentiating \( 100 \log x \) with respect to \( x \) gives: \[ \frac{d}{dx} (100 \log x) = \frac{100}{x}. \] Thus, the correct answer is option (C) \( \frac{100}{x} \).