- Calculus, Volume 1: One Variable Calculus, with an Introduction to Linear Algebra
- Tom M. Apostol
- Second Edition
- 1967
- 978-1-119-49673-1
14.4 Exercises
- Compute the derivatives $F'(t)$ and $F''(t)$ for: $F(t) = (\cos t, \sin^2 t, \sin 2t, \tan t)$
- Recall from section 2.5 that: $2\ \text{sin}(t)\text{cos}(t) = \text{sin}(2t).$
- $$\displaylines{F'(t) &= (-\text{sin}(t), 2\ \text{sin}(t)\text{cos}(t), 2\ \text{cos}(2t), \text{sec}^2(t)) \\ &= (-\text{sin}(t), \text{sin}(2t), 2\ \text{cos}(2t), \text{sec}^2(t))}$$ $$\displaylines{F''(t) &= (-\text{cos}(t), 2\text{cos}(2t), -4\text{sin}(2t), 2\text{sec}^2(t)\text{tan}(t))}$$