Calculus Derivatives and Decreasing Intervals Quiz
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Questions and Answers

What is the derivative of $f(x) = -3x^2 + 7x - 15 + \frac{1}{x}$?

  • $f'(x) = -6x + 7 - \frac{1}{x^2}$ (correct)
  • $f'(x) = -6x + 7 + \frac{1}{x}$
  • $f'(x) = -6x + 7 + \frac{1}{x^2}$
  • $f'(x) = -6x + 7 - \frac{1}{x}$

    • What is the derivative of $f(x) = (\cos(x) + 2x)(x^3 - 5)^4$?

  • $f'(x) = -4(\cos(x) + 2x)(x^3 - 5)^3\sin(x) + 4(\cos(x) + 2x)3(x^3 - 5)^4$
  • $f'(x) = -4(\cos(x) + 2x)(x^3 - 5)^3\sin(x) + (\cos(x) + 2x)3(x^3 - 5)^4$
  • $f'(x) = -4(\cos(x) + 2x)(x^3 - 5)^3\sin(x) + 4(\cos(x) + 2x)(x^3 - 5)^4$ (correct)
  • $f'(x) = -4(\cos(x) + 2x)(x^3 - 5)^3\sin(x) + (\cos(x) + 2x)3(x^3 - 5)^3$

    • What is the derivative of $f(x) = \cos(2x)x^4 + 1$?

  • $f'(x) = -2\sin(2x)x^4 + 4x^3$ (correct)
  • $f'(x) = -2\sin(2x)x^4 - 8x^3$
  • $f'(x) = -2\sin(2x)x^3 - 8x^3$
  • $f'(x) = -2\sin(2x)x^3 + 4x^3$

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