Find the Derivative - d/dx log base 12 of x

Problem

d()/d(x)*(log_12)(x)

Solution

1. Apply the change of base formula to rewrite the logarithm in terms of the natural logarithm, ln(x)

(log_12)(x)=ln(x)/ln(12)

2. Identify the constant factor in the expression to prepare for differentiation.

d()/d(x)ln(x)/ln(12)=1/ln(12)d(ln(x))/d(x)

3. Apply the derivative rule for the natural logarithm, which states d(ln(x))/d(x)=1/x

1/ln(12)⋅1/x

4. Simplify the expression by multiplying the fractions.

1/(x*ln(12))

Final Answer

d((log_12)(x))/d(x)=1/(x*ln(12))

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