Find the Derivative - d/dx log of 3x

Problem

d((log_)(3*x))/d(x)

Solution

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

2. Apply the chain rule by setting u=3*x The derivative of u with respect to x is (d(3)*x)/d(x)=3

3. Substitute the values into the derivative formula for logarithms.

d((log_10)(3*x))/d(x)=1/(3*x*ln(10))⋅3

4. Simplify the expression by canceling the constant factor 3 from the numerator and denominator.

3/(3*x*ln(10))=1/(x*ln(10))

Final Answer

d((log_)(3*x))/d(x)=1/(x*ln(10))

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