Find the Derivative - d/dx log base 13 of x

Problem

d()/d(x)*(log_13)(x)

Solution

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

(log_13)(x)=ln(x)/ln(13)

2. Identify the constant factor in the expression, which is 1/ln(13)

d()/d(x)ln(x)/ln(13)=1/ln(13)d(ln(x))/d(x)

3. Differentiate the natural logarithm using the rule d(ln(x))/d(x)=1/x

1/ln(13)⋅1/x

4. Simplify the expression by multiplying the fractions.

1/(x*ln(13))

Final Answer

d((log_13)(x))/d(x)=1/(x*ln(13))

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