504QuotientRule

The Quotient Rule

Use when 2 functions are divided math \dfrac{d}{dx} \left( \dfrac{u}{v} \right) = \dfrac {v \times \dfrac {du}{dx} - u \times \dfrac {dv}{dx}}{v^2} math

Example math y=\dfrac{(x^2+3x-6)}{\sin(6x)} math

math \\ \text{Let } u = x^2+3x-6 \\ \dfrac {du}{dx} = 2x+3 math and math \\ \text{Let } v = \sin (6x) \\ \dfrac {dv}{dx} = 6\cos (6x) math

Now use **u** and **v** in the Quotient Rule math \dfrac{d}{dx} \left( \dfrac{u}{v} \right) = \dfrac {v \times \dfrac {du}{dx} - u \times \dfrac {dv}{dx}}{v^2} math

math \dfrac{d}{dx} \left( \dfrac{u}{v} \right) = \dfrac {\sin(6x)(2x+3) - (x^2+3x-6)(6\cos(6x))}{\sin^2(6x)} math

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