Find d/dx 5x^2 - 3x + 2: animated lesson

1. 1. The problem
   Finding a derivative

   $\frac{d}{dx}\left[5{x}^{2}-3x+2\right]$
2. 2. Steps, part 1
   1. $$\frac{d}{dx}\left[5{x}^{2}-3x+2\right] = 10x-3$$
      Sum rule: differentiate each term separately
   2. $$\frac{d}{dx}\left[5{x}^{2}-3x\right] = 10x-3$$
      Difference rule: differentiate each term separately
   3. $$\frac{d}{dx}\left[3x\right] = 3$$
      Constant multiple rule
   4. $$\frac{d}{dx}\left[5{x}^{2}\right] = 10x$$
      Constant multiple rule
3. 3. Steps, part 2
   1. $$\frac{d}{dx}\left[{x}^{2}\right] = 2x$$
      Power rule: d/dx[xⁿ] = n·xⁿ⁻¹
   2. $$f'(x) = 10x-3$$
      Combine and simplify
4. 4. The answer
   $$f'(x) = 10x-3$$

   f'(x) = 10x - 3

5. 5. 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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