Apentix/AP Calculus AB/Unit 2: Differentiation: Definition and Basic Derivative Rules/Question
AP Calculus ABhardmcq1 pt

If f(x)=x3ln⁡xf(x)=x^3\ln x, then f′(x)=f'(x)=

A.3x2ln⁡x3x^2\ln x
B.3x2⋅1x3x^2\cdot\dfrac{1}{x}
C.3x2ln⁡x+x33x^2\ln x+x^3
D.x2(3ln⁡x+1)x^2(3\ln x+1)

Explanation

Core Concept

The product rule gives 3x2ln⁡x+x3⋅1x3x^2\ln x+x^3\cdot\dfrac{1}{x}. Simplifying, this is 3x2ln⁡x+x2=x2(3ln⁡x+1)3x^2\ln x+x^2=x^2(3\ln x+1).

Correct Answer

Dx2(3ln⁡x+1)x^2(3\ln x+1)

More Unit 2: Differentiation: Definition and Basic Derivative Rules practice questions

Try a random question →

Practice more AP Calculus AB questions with full explanations

Practice Unit 2: Differentiation: Definition and Basic Derivative Rules Questions →