The quotient rule is a formula for taking the derivative of a quotient of two functions. This formula makes it somewhat easier to keep track of all of the terms. If $u(x)$ and $v(x)$ are two functions of $x$ and $\displaystyle f(x)=\dfrac{u(x)}{v(x)}$, then $$f^{\prime}(x)=\dfrac{u^{\prime}(x)v(x)-u(x)v^{\prime}(x)}{v(x)^2}$$ Expressions like $\displaystyle \dfrac{x^2+x+1}{4x-2}$, $\displaystyle \dfrac{\sqrt{x+2}}{x^2-4}$ and $\displaystyle \dfrac{x^4}{(x^3-x^2-1)^5}$ are called […]

The following examples show that you do not need to apply the quotient rule for differentiating when the denominator is constant. Please see the following cases with the same question. $\textit{Application of the quotient rule}$ \( \begin{align} \displaystyle\dfrac{d}{dx}\dfrac{48x – 4x^3}{3} &= \frac{{\frac{d}{{dx}}\left( {48x – 4{x^3}} \right) \times 3 – \left( {48x – 4{x^3}} \right) \times […]