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Exercise 8

Avg difficulty 2.5

Determine the derivative of each of the following functions. Use proper notation and clearly identify the derivative rules you use.

  1. f(x)=ln⁡(2arctan⁡(x)+3arcsin⁡(x)+5)f(x) = \ln(2\arctan(x) + 3\arcsin(x) + 5)

  2. r(z)=arctan⁡(ln⁡(arcsin⁡(z)))r(z) = \arctan(\ln(\arcsin(z)))

  3. q(t)=arctan⁡2(3t)arcsin⁡4(7t)q(t) = \arctan^2(3t) \arcsin^4(7t)

  4. g(v)=ln⁡(arctan⁡(v)arcsin⁡(v)+v2)g(v) = \ln\left( \frac{\arctan(v)}{\arcsin(v) + v^2} \right)

Boelkins, Active Calculus, §2.6 Derivatives of inverse functions, Exercise 8

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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.