Find the Derivative - d/dx log of 9x

Problem

d((log_)(9*x))/d(x)

Solution

1. Identify the function as a common logarithm, which has a base of 10 The derivative rule for (log_b)(u) is 1/(u*ln(b))⋅d(u)/d(x)

2. Apply the chain rule by setting u=9*x The derivative of u with respect to x is 9

3. Substitute the values into the derivative formula:

d((log_10)(9*x))/d(x)=1/(9*x*ln(10))⋅9

4. Simplify the expression by canceling the constant factor 9 in the numerator and denominator.

9/(9*x*ln(10))=1/(x*ln(10))

Final Answer

d((log_)(9*x))/d(x)=1/(x*ln(10))

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