Quotient Rule Formula

In calculus, Quotient rule is helps govern the derivative of a quotient with existing derivatives. There are some steps to be followed for finding out the derivative of a quotient.

Now, consider two expressions with is in

\begin{array}{l} \frac{u}{v} \end{array}

form q is given as quotient rule formula.

\begin{array}{l} \frac{d}{d x} (\frac{u}{v}) = \frac{v \frac{d u}{d x} - u \frac{d v}{d x}}{v^{2}} \end{array}

Solved example

Question: Differentiate

\begin{array}{l} \frac{2}{x + 1} \end{array}

Solution:

Given equation is:

\begin{array}{l} \begin{matrix} \frac{d}{d x} (\frac{u}{v}) = \frac{d}{d x} (\frac{2}{x + 1}) \\ = \frac{(x + 1) \frac{d}{d x} (2) - 2 \frac{d}{d x} (x + 1)}{(x + 1)^{2}} \\ = \frac{(x + 1) \times 0 - 2 (1)}{(x + 1)^{2}} \\ = \frac{- 2}{(x + 1)^{2}} \end{matrix} \end{array}

Quotient Rule Formula

Solved example

Comments

Leave a Comment Cancel reply