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 […]

# Tag Archives: Quotient Rule

# 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 […]

# Finding a Function from Differential Equation

The solution of a differential equation is to find an expression without \( \displaystyle \frac{d}{dx} \) notations using given conditions.Note that the proper rules must be in place in order to achieve the valid solution of the differential equations, such as product rule, quotient rule and chain rule particularly.Many students missed applying the chain rule […]