Find the Derivative - d/dx natural log of (x)^3

Problem

d l n x cubed over 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 l n u over d x equals 1 over u times d u over d x

3. Substitute u equals x cubed into the chain rule formula.

4. Differentiate the inner function x cubed using the power rule to get 3 x squared

5. Multiply the results together to get the fraction with numerator 1 and denominator x cubed times 3 x squared

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

Final Answer

d l n x cubed over d x equals 3 over x

Want more problems? Check here!