Product Rule

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See: Calculus, Chain Rule, Bayes Theorem.


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    • In calculus, the product rule is a formula used to find the derivatives of products of two or more functions. It may be stated thus: [math](f\cdot g)'=f'\cdot g+f\cdot g' \,\! [/math] or in the Leibniz notation thus: [math]\dfrac{d}{dx}(u\cdot v)=u\cdot \dfrac{dv}{dx}+v\cdot \dfrac{du}{dx}[/math].

      The derivative of the product of three functions is: [math]\dfrac{d}{dx}(u\cdot v \cdot w)=\dfrac{du}{dx} \cdot v \cdot \lt math\gt w[/math] + u \cdot \dfrac{dv}{dx} \cdot [math]w[/math] + u\cdot v\cdot \dfrac{dw}{dx}</math>.