Vipul at 22:55, 21 September 2011

2011-09-21T22:55:09Z

← Older revision		Revision as of 22:55, 21 September 2011
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	<math>\frac{d}{dx} \left(\frac{f(x)}{g(x)}\right) = \frac{g(x)f'(x) - f(x)g'(x)}{(g(x))^2}</math>		<math>\frac{d}{dx} \left(\frac{f(x)}{g(x)}\right) = \frac{g(x)f'(x) - f(x)g'(x)}{(g(x))^2}</math>

			==Related rules==

			* [[Product rule for differentiation]]
			* [[Second derivative rule for parametric descriptions]] (uses the quotient rule in its proof)
			* [[Quotient rule for second derivative]]

Vipul: Created page with "{{differentiation rule}} ==Statement== Suppose $f$ and $g$ are functions defined at and around a point $x_0$ and they are both differentiab..."

2011-09-05T13:52:49Z

Created page with "{{differentiation rule}} ==Statement== Suppose <math>f</math> and <math>g</math> are functions defined at and around a point <math>x_0</math> and they are both differentiab..."

New page

{{differentiation rule}}

==Statement==

Suppose <math>f</math> and <math>g</math> are [[function]]s defined at and around a point <math>x_0</math> and they are both differentiable at <math>x_0</math> (i.e., the [[derivative]]s <math>f'(x_0)</math> and <math>g'(x_0)</math> are defined) and <math>g(x_0) \ne 0</math>. Then, the [[pointwise quotient of functions|quotient]] <math>f/g</math> is differentiable at <math>x_0</math>, and its derivative is given as follows:

<math>\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right)|_{x = x_0} = \frac{g(x_0)f'(x_0) - f(x_0)g'(x_0)}{(g(x_0))^2}</math>

If we consider the general expressions rather than the evaluation at a particular point <math>x_0</math>, we can rewrite the above as:

<math>\frac{d}{dx} \left(\frac{f(x)}{g(x)}\right) = \frac{g(x)f'(x) - f(x)g'(x)}{(g(x))^2}</math>

Quotient rule for differentiation - Revision history

Vipul at 22:55, 21 September 2011

Vipul: Created page with "{{differentiation rule}} ==Statement== Suppose f and g are functions defined at and around a point x_0 and they are both differentiab..."

Vipul: Created page with "{{differentiation rule}} ==Statement== Suppose $f$ and $g$ are functions defined at and around a point $x_0$ and they are both differentiab..."