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Easy: Polynomials
The power rule: the derivative of xⁿ is nxⁿ⁻¹. Bring the exponent down as a coefficient and lower the exponent by one. A constant times a function keeps its constant, a sum is differentiated term by term, and the derivative of a constant is 0. Rewrite roots and fractions as powers first: √x = x^(1/2) and 1/x² = x^(−2).
Find the derivative.
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Rewrite them as powers first: √x = x^(1/2) and 1/x² = x⁻². Then the power rule gives (1/2)x^(−1/2) and −2x⁻³.
0. A constant doesn't change, so its rate of change is 0. That's why the constant term disappears when differentiating a polynomial.
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