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Derivatives with the power rule
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Learn it d/dx(xⁿ) = nxⁿ⁻¹, for any real n. Constants multiply through, sums differentiate term by term, and the derivative of a constant is 0. Rewrite roots and fractions as powers first: √x = x^½, 1/x² = x⁻².
Example: f(x) = 4x³ − 6√x + 7. Find f′(x).
- 4·3x² − 6·½x^(−½) + 0.
- f′(x) = 12x² − 3/√x.
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