Find d/dx sin(3x): animated lesson

1. 1. The problem
   Finding a derivative

   $\frac{d}{dx}\left[\sin\left(3x\right)\right]$
2. 2. Step by step
   1. $$\frac{d}{dx}\left[\sin\left(3x\right)\right] = 3\cos\left(3x\right)$$
      Chain rule — d/dx[sin u] = cos u · u′
   2. $$\frac{d}{dx}\left[3x\right] = 3$$
      Constant multiple rule
   3. $$f'(x) = 3\cos\left(3x\right)$$
      Combine and simplify
3. 3. The answer
   $$f'(x) = 3\cos\left(3x\right)$$

   f'(x) = 3cos(3x)

4. 4. Check
   • ✓Cross-checked numerically against an independent symbolic differentiator at 8 sample points ✓

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