Differentiate ln(sin(x)): animated lesson

1. 1. The problem
   Finding a derivative

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

   f'(x) = cos(x) / sin(x)

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

Differentiate with the power, product, quotient and chain rules, including higher derivatives.

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