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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 $\frac{u}{v}$ form q is given as quotient rule formula.

\[\large \frac{d}{dx}\left(\frac{u}{v}\right)=\frac{v\tfrac{du}{dx}-u\tfrac{dv}{dx}}{v^{2}}\]

Solved example

Question: Differentiate $\frac{2}{x+1}$ ?

Solution:

Given equation is:

$\frac{d}{dx}\left(\frac{u}{v}\right)\left(\frac{2}{x+1}\right)$

$=\frac{\frac{(x+1)d2}{dx}-2\tfrac{d(x+1)}{dx}}{(x+1)^{2}}$

$=\frac{(x+1)x\,0-2×1}{(x+1)^{2}}$

$=\frac{-2}{(x+1)^{2}}$

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