Question

Find the derivative of \( \log(x^9) \).

• A. \( \frac{1}{9x} \)
• B. \( \frac{1}{x} \)
• C. \( \frac{9}{x} \)
• D. \( \frac{1}{x} \log 5 \)

Answer 1

The Correct Option is C

We have the function \( f(x) = \log(x^9) \). Using the properties of logarithms, we can simplify the function: \[ \log(x^9) = 9 \log(x) \] Now, we take the derivative of this with respect to \( x \): \[ \frac{d}{dx} \left( 9 \log(x) \right) = 9 \times \frac{1}{x} \] Thus, the derivative is: \[ \frac{9}{x} \] Therefore, the correct answer is \( \frac{9}{x} \), which corresponds to option (C).