Find the Derivative - d/dx natural log of (x)^2

Problem

d(ln(x2))/d(x)

Solution

1. Identify the function as a composition of the natural logarithm and a power function, which requires the use of the chain rule.

2. Apply the chain rule for the natural logarithm, which states that d(ln(u))/d(x)=1/u⋅d(u)/d(x)

3. Substitute u=x2 into the chain rule formula.

4. Differentiate the inner function x2 with respect to x to get 2*x

5. Multiply the results to get 1/(x2)⋅2*x

6. Simplify the expression by canceling x from the numerator and denominator.

Final Answer

d(ln(x2))/d(x)=2/x

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