503ProductRule

The Product Rule

Use when 2 functions are multiplied together math \dfrac{d}{dx} \left( uv \right) = u \times \dfrac {dv}{dx} + v \times \dfrac {du}{dx} math

Example math y = (x^2+3x-6)sin(6x) math

math \\ \text{Let } u = x^2+3x-6 \\ \dfrac {du}{dx} = 2x+3 math

math \\ \text{Let } v = \sin (6x) \\ \dfrac {dv}{dx} = 6\cos (6x) math

Now use **u** and **v** in the Product Rule math \dfrac{d}{dx} \left( uv \right) = u \times \dfrac {dv}{dx} + v \times \dfrac {du}{dx} math math \\ \dfrac{d}{dx} \left( uv \right) = (x^2+3x-6) \times 6\cos(6x) + (2x+3) \times \sin(6x) \\ \\ \dfrac{d}{dx} \left( uv \right) = 6(x^2+3x-6) \cos(6x) + (2x+3) \sin(6x) math

**See also** [|www.mathsonline.com.au] Y12Advanced --> Calculus --> Introductory Calculus --> Lesson 4