Find the Derivative - d/d@VAR f(x) = natural log of x^3

Problem

d(ln(x3))/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, where d(ln(u))/d(x)=1/u⋅d(u)/d(x)

3. Substitute u=x3 into the derivative formula.

4. Differentiate the inner function x3 using the power rule to get 3*x2

5. Multiply the results to get 1/(x3)⋅3*x2

6. Simplify the expression by canceling the common x2 terms in the numerator and denominator.

Final Answer

d(ln(x3))/d(x)=3/x

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