Derivative of ln(x) using logarithmic differentiation: Step-by-step Guide

Derivative of ln (x)

To find the derivative of ln(x), we can use the rules of logarithmic differentiation

To find the derivative of ln(x), we can use the rules of logarithmic differentiation.

Step 1: Start with the function f(x) = ln(x).
Step 2: Take the natural logarithm of both sides:
ln(f(x)) = ln(ln(x)).
Step 3: Differentiate both sides implicitly with respect to x:
(1/f(x)) * f'(x) = (1/x)
Step 4: Solve for f'(x):
f'(x) = x / f(x).
Step 5: Replace f(x) with ln(x):
f'(x) = x / ln(x).

Therefore, the derivative of ln(x) is x / ln(x).

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Derivative of ln(x) using logarithmic differentiation: Step-by-step Guide