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

Problem

d(ln(x^3))/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=x^3 into the derivative formula.

4. Differentiate the inner function x^3 using the power rule to get 3*x^2

5. Multiply the results to get 1/(x^3)⋅3*x^2

6. Simplify the expression by canceling the common x^2 terms in the numerator and denominator.

Final Answer

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

Want more problems? Check here!