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The Chain Rule (Calculus I)

Free printable university Calculus I worksheet: differentiating composite functions with the chain rule, including powers, roots and negative powers of inner functions. Every derivative cross-checked numerically.

✓ Answer key checked by math, never wrong
Calculus I · Math worksheet
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The Chain Rule

Differentiate each composite function with the chain rule: identify the outer function and the inner function u, then compute f' = (outer)'(u) · u'.

  1. 1.
    Differentiate f(x) = (−x+4)4(-x + 4)^{4} using the chain rule.
  2. 2.
    Differentiate f(x) = (−3x+4)5(-3x + 4)^{5} using the chain rule.
  3. 3.
    Differentiate f(x) = (−x+2)6(-x + 2)^{6} using the chain rule.
  4. 4.
    Differentiate f(x) = (−x2+2x−4)4(-x^{2} + 2x - 4)^{4} using the chain rule.
  5. 5.
    Differentiate f(x) = (2x2+3)5(2x^{2} + 3)^{5} using the chain rule.
  6. 6.
    Differentiate f(x) = (−4x2−×−3)4(-4x^{2} - \times - 3)^{4} using the chain rule.
  7. 7.
    Differentiate f(x) = x2+4\sqrt{x^{2} + 4}.
  8. 8.
    Differentiate f(x) = x2+7\sqrt{x^{2} + 7}.
  9. 9.
    Differentiate f(x) = 1/(x2+4)2(x^{2} + 4)^{2}.
  10. 10.
    Differentiate f(x) = 1/(x2+5)2(x^{2} + 5)^{2}.
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