Mastering Anti-Derivatives and ln Functions
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Questions and Answers

Which of the following is the anti-derivative of the function $f(x) = 3x^2 + 4x + 5$?

  • $F(x) = 3x^3 + 4x^2 + 5x + C$
  • $F(x) = 3x^2 + 4x + 5 + C$
  • $F(x) = \frac{3},{2}x^3 + 2x^2 + 5x + C$
  • $F(x) = x^3 + 2x^2 + 5x + C$ (correct)

    • Which of the following is equivalent to $e^{2\ln(x)}$?

  • $x^{2\ln(2)}$
  • $2^x$
  • $x^2$ (correct)
  • $2x$

    • What is the derivative of the function $f(x) = \ln(2x)$?

  • $f'(x) = \ln(x)$
  • $f'(x) = \frac{2},{x}$
  • $f'(x) = \frac{1},{2x}$
  • $f'(x) = \frac{1},{x}$ (correct)

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