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Product Rule

Jan 11, 20241 min read

Product Rule

Definition of Product Rule:

*Created on 23:09 11-01-2024

In calculus, the product rule (or Leibniz ruleor Leibniz product rule) is a formula used to find the derivatives of products of two or more functions. For two functions, it may be stated in Lagrange’s notation as

( u ⋅ v ) ′ = u ′ ⋅ v + u ⋅ v ′

{\displaystyle (u\cdot v)'=u'\cdot v+u\cdot v'}

or in Leibniz’s notation as

d d x ( u ⋅ v ) = d u d x ⋅ v + u ⋅ d v d x .

{\displaystyle {\frac {d}{dx}}(u\cdot v)={\frac {du}{dx}}\cdot v+u\cdot {\frac {dv}{dx}}.}

The rule may be extended or generalized to products of three or more functions, to a rule for higher-order derivatives of a product, and to other contexts.

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