Find d/dx ln(cos(x)): animated lesson

1. 1. The problem
   Finding a derivative

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

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