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Product and Quotient Rules (Calculus I)

Free printable university Calculus I worksheet: the power rule with negative and fractional exponents, and the product and quotient rules, including products with trigonometric factors. Every derivative cross-checked numerically.

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Calculus I · Math worksheet
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Product and Quotient Rules

Differentiate each function. Use (uv)' = u'v + uv' for products and (u/v)' = (u'v - uv')/v^2 for quotients; simplify your answers where asked.

  1. 1.
    Differentiate f(x) = -2x^3 - 2/x - 2√x by writing every term as a power of x first.
  2. 2.
    Differentiate f(x) = 2x^4 + 4/x + 2√x by writing every term as a power of x first.
  3. 3.
    Differentiate f(x) = (-2x^2 - 2x + 4)(2x - 1) using the product rule; expand and simplify your answer.
  4. 4.
    Differentiate f(x) = (-2x^2 + 3x - 2)(-4x^2 + 5x - 1) using the product rule; expand and simplify your answer.
  5. 5.
    Differentiate f(x) = (-2x^2 - 3x - 2)(-2x + 3) using the product rule; expand and simplify your answer.
  6. 6.
    Differentiate f(x) = x sin(x) using the product rule.
  7. 7.
    Differentiate f(x) = x2x^{2} cos(x) using the product rule.
  8. 8.
    Differentiate f(x) = (-3x - 2) / (3x + 1) using the quotient rule.
  9. 9.
    Differentiate f(x) = (-x) / (2x + 1) using the quotient rule.
  10. 10.
    Differentiate f(x) = (-2x^2 + x + 4) / (x + 2) using the quotient rule; simplify the numerator.
  11. 11.
    Differentiate f(x) = (3x^2 - 4x - 3) / (x - 1) using the quotient rule; simplify the numerator.
  12. 12.
    Differentiate f(x) = (x2x^{2} - 4x) / (x + 1) using the quotient rule; simplify the numerator.
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