Find the derivative of log(x): animated lesson

1. 1. The problem
   Finding a derivative

   $\frac{d}{dx}\left[\log_{10}\left( x\right)\right]$
2. 2. Step by step
   1. $$\frac{d}{dx}\left[\log_{10}\left( x\right)\right] = \frac{\frac{1}{\ln\left(10\right)}}{x}$$
      d/dx[log₁₀ x] = 1/(x ln 10)
   2. $$f'(x) = \frac{\frac{1}{\ln\left(10\right)}}{x}$$
      Combine and simplify
3. 3. The answer
   $$f'(x) = \frac{\frac{1}{\ln\left(10\right)}}{x}$$

   f'(x) = 1 / ln(10) / 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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