The bproduct rule/b is used for differentiating functions multiplied by each other.

(y = f(x)g(x) )

(\boxed{\dfrac{dy}{dx} = f'(x)g(x) + f(x)g'(x)} )

Using substitution, if (u = f(x) ) and (v = g(x) ), then:

(\boxed{\dfrac{dy}{dx} = \dfrac{du}{dx}v + u\dfrac{dv}{dx}} )

Tip: Think of it as "ithe derivative of the first function, multiplied by the second function, plus the first function multiplied by the derivative of the second function/i".

[b]uProduct rule[/u]/b

(\dfrac{dy}{dx} = f'(x)g(x) + f(x)g'(x) )

(\dfrac{dy}{dx} = \dfrac{du}{dx}v + u\dfrac{dv}{dx} )