Tag Archives: Quotient Rule

Quotient Rule Differentiation

Quotient Rule Differentiation

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 […]

When No Need to Apply Quotient Rule for Differentiating a Fraction

When No Need to Apply Quotient Rule for Differentiating a Fraction

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 […]