Question:
Find the derivative of \( \log(x^9) \).
Find the derivative of \( \log(x^9) \).
Updated On: Sep 13, 2025
- \( \frac{1}{9x} \)
- \( \frac{1}{x} \)
- \( \frac{9}{x} \)
- \( \frac{1}{x} \log 5 \)
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The Correct Option is C
Solution and Explanation
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).
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