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product rule

The rule for differentiating a product of two functions — it is not just the product of the derivatives.

For f(x)=u(x)v(x), f'(x) = u'(x)v(x) + u(x)v'(x) — differentiate the first factor times the second, plus the first times the derivative of the second.

Examples

  • For f(x)=x^2\sin x: f''(x) = 2x\sin x + x^2\cos x.

See also

derivative quotient rule
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