The quotient rule is used to differentiate fractions which contain a function of x in the numerator and denominator and that cannot be divided easily.
It is an important rule that is used extensively in calculus. In the tutorial I show you what it is and how to apply it.

Quotient Rule:

  • \text{If } y = \dfrac{u}{v} \\ \\ \text{then } \dfrac{dy}{dx} = \dfrac{v \dfrac{du}{dx} - u \dfrac{dv}{dx}}{v^2}

Proof of Quotient Rule


The next example is more challenging in as much as it requires the use of the chain rule within the question and aims to reinforce the need for a systematic approach to simplifying the answer.
Well worth doing before looking at the video worked solution.

\text{Find } \dfrac{dy}{dx} \text{ where}:

  1. y = \dfrac{(3x^2 -1)^4}{(5x-2)^3}