Polynomial Derivative
d/dx(aₙxⁿ + … + a₁x + a₀) = naₙxⁿ⁻¹ + … + a₁. Power rule.
Result
f'(x)
3x² − 6x + 5
f(2) = 13.0000; f'(2) = 5.0000.
- f(x)1x³ − 3x² + 5x + 7
- f'(x)3x² − 6x + 5
- f(2)13.000000
- f'(2)5.000000
- Slope at x5.000000
Step-by-step
- Apply power rule: d/dx(xⁿ) = n·xⁿ⁻¹.
- f'(x) = 3x² − 6x + 5.
- Evaluate: f'(2) = 5.0000.
How to use this calculator
- Enter polynomial coefficients.
- Optional: evaluate at x.
About this calculator
Power rule: d/dx(xⁿ) = n·xⁿ⁻¹. Constant rule: d/dx(c) = 0. Sum rule: derivative of sum = sum of derivatives. Polynomial differentiation is mechanical: drop the exponent into the coefficient, decrement exponent. Used for finding slopes (tangent lines), velocity from position, optimization (set f' = 0). Source: Wolfram MathWorld - Polynomial Derivative.
Frequently asked
d/dx(xⁿ) = n·xⁿ⁻¹. Foundation of polynomial differentiation.
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