Find d/dx (3x + 1)^4: animated lesson

1. 1. The problem
   Finding a derivative

   $\frac{d}{dx}\left[{\left(3x+1\right)}^{4}\right]$
2. 2. Step by step
   1. $$\frac{d}{dx}\left[{\left(3x+1\right)}^{4}\right] = 12 {\left(3x+1\right)}^{3}$$
      Power rule with the chain rule: d/dx[uⁿ] = n·uⁿ⁻¹·u′
   2. $$\frac{d}{dx}\left[3x+1\right] = 3$$
      Sum rule: differentiate each term separately
   3. $$\frac{d}{dx}\left[3x\right] = 3$$
      Constant multiple rule
   4. $$f'(x) = 12 {\left(3x+1\right)}^{3}$$
      Combine and simplify
3. 3. The answer
   $$f'(x) = 12 {\left(3x+1\right)}^{3}$$

   f'(x) = 12(3 x + 1)³

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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