Derivative of x³ ln x

Problem

Differentiate $f(x)=x^3\ln x$ (product rule).

Solution

With $(f\cdot g)' = f'g + fg'$, setting $f=x^3$ and $g=\ln x$: $f'(x) = 3x^2\ln x + x^3\cdot\frac{1}{x} = 3x^2\ln x + x^2 = \boxed{x^2(3\ln x + 1)}.$

Links

Topics: Derivatives
Concepts: Derivative · Rules of differentiation
Skills: Differentiate
Exercise type: Derivative computation