Product rule

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${\displaystyle \int _{a}^{b}f'(t)\,dt=f(b)-f(a)}$
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In calculus, the product rule (or Leibniz rule^[1] or 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

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

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

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.