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Back to The chain rule

Exercise 12

Avg difficulty 2.5

Let u(x)u(x) be a differentiable function. For each of the following functions, determine the derivative. Each response will involve uu and/or u′u'.

  1. p(x)=eu(x)p(x) = e^{u(x)}

  2. q(x)=u(ex)q(x) = u(e^x)

  3. r(x)=cot⁡(u(x))r(x) = \cot(u(x))

  4. s(x)=u(cot⁡(x))s(x) = u(\cot(x))

  5. a(x)=u(x4)a(x) = u(x^4)

  6. b(x)=(u(x))4b(x) = (u(x))^4

Boelkins, Active Calculus, §2.5 The chain rule, Exercise 12

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Adapted from Active Calculus © 2012–2025 Matthew Boelkins. Licensed under CC BY-SA 4.0. Source: Active Calculus. Imported at revision dc86ba3.