Find the Derivative - d/dy natural log of y^2

Problem

d(ln(y2))/d(y)

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 by taking the derivative of the outer function ln(u) with respect to u=y2 which is 1/u

3. Multiply by the derivative of the inner function y2 with respect to y which is 2*y

4. Combine the results to get 1/(y2)⋅2*y

5. Simplify the expression by canceling a factor of y from the numerator and denominator.

Final Answer

d(ln(y2))/d(y)=2/y

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