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

1. 1. The problem
   Finding a derivative

   $\frac{d}{dx}\left[\frac{\cos\left( x\right)}{x}\right]$
2. 2. Step by step
   1. $$\frac{d}{dx}\left[\frac{\cos\left( x\right)}{x}\right] = -\frac{\sin\left( x\right)+\frac{\cos\left( x\right)}{x}}{x}$$
      Quotient rule: (u/v)′ = (u′v − uv′)/v²
   2. $$\frac{d}{dx}\left[\cos\left( x\right)\right] = -\sin\left( x\right)$$
      d/dx[cos x] = −sin x
   3. $$f'(x) = -\frac{\sin\left( x\right)+\frac{\cos\left( x\right)}{x}}{x}$$
      Combine and simplify
3. 3. The answer
   $$f'(x) = -\frac{\sin\left( x\right)+\frac{\cos\left( x\right)}{x}}{x}$$

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