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Back to The chain rule

Activity 2.5.3

Avg difficulty 2.5

For each of the following functions, find the function's derivative. State the rule(s) you use, label relevant derivatives appropriately, and be sure to clearly identify your overall answer.

  1. p(r)=4r6+2erp(r) = 4\sqrt{r^6 + 2e^r}

  2. m(v)=sin⁡(v2)cos⁡(v3)m(v) = \sin(v^2) \cos(v^3)

  3. h(y)=cos⁡(10y)e4y+1h(y) = \frac{\cos(10y)}{e^{4y}+1}

  4. s(z)=2z2sec⁡(z)s(z) = 2^{z^2 \sec (z)}

  5. c(x)=sin⁡(ex2)c(x) = \sin(e^{x^2})

Boelkins, Active Calculus, §2.5 The chain rule, Activity 2.5.3

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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.