How do you find the derivative of a function?
Quick answer
The derivative measures the rate at which a function changes — the slope of its graph at a point. For most functions you use standard rules rather than first principles.
Key rules: power rule d/dx(xⁿ) = n·xⁿ⁻¹; constant rule d/dx(c) = 0; sum rule (differentiate term by term); product rule (uv)' = u'v + uv'; quotient rule; and chain rule for composite functions.
Example: d/dx(3x² + 2x − 5) = 6x + 2. Example with chain rule: d/dx(sin(2x)) = 2·cos(2x).
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