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What is the derivative of x³ ln(x) with respect to x?
  1. 3x² ln(x) + x²
  2. x² + 3x² ln(x)
  3. x³ + ln(x)
  4. None of these
Explanation

We use the product rule since it's the product of two functions:


f(x) = x^3 cdot ln(x)

Let:


  • u = x^3 Rightarrow u' = 3x^2


  • v = ln(x) Rightarrow v' = frac{1}{x}

Apply the product rule:

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