Quotient Rule Formula

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.

\(\begin{array}{l}\frac{d}{dx}\left(\frac{u}{v}\right)=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^{2}}\end{array} \)

Solved example

Question: Differentiate 

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


Given equation is:

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


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