Differentiation rule for power functions - Revision history

Vipul at 03:14, 26 May 2014

2014-05-26T03:14:12Z

← Older revision		Revision as of 03:14, 26 May 2014
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	{\| class="sortable" border="1"		{\| class="sortable" border="1"
	! Case on <math>r</math> !! Values of <math>x</math> for which this makes sense		! Case on <math>r</math> !! Values of real <math>x</math> for which this makes sense
	\|-		\|-
	\| <math>r = 0</math> \|\| all nonzero <math>x</math>. Also makes sense at <math>x = 0</math> if we interpret the left side as 1 (constant equal to the list at 0) and the right side as 0.		\| <math>r = 0</math> \|\| all nonzero <math>x</math>. Also makes sense at <math>x = 0</math> if we interpret the left side as 1 (constant equal to the list at 0) and the right side as 0.

Vipul at 03:13, 26 May 2014

2014-05-26T03:13:56Z

← Older revision		Revision as of 03:13, 26 May 2014
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	! Case on <math>r</math> !! Values of <math>x</math> for which this makes sense		! Case on <math>r</math> !! Values of <math>x</math> for which this makes sense
	\|-		\|-
	\| <math>r = 0</math> \|\| all nonzero <math>x</math>. Also makes sense at <math>x = 0</math> if we interpret the right side as 0.		\| <math>r = 0</math> \|\| all nonzero <math>x</math>. Also makes sense at <math>x = 0</math> if we interpret the left side as 1 (constant equal to the list at 0) and the right side as 0.
	\|-		\|-
	\| <math>r</math> a rational number with odd denominator and greater than or equal to 1 \|\| All <math>x</math>		\| <math>r</math> a rational number with odd denominator and greater than or equal to 1 \|\| All <math>x</math>

Vipul: /* Statement */

2011-12-19T17:11:50Z

Statement

← Older revision		Revision as of 17:11, 19 December 2011
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	where <math>r</math> is a constant. Some notes on the validity:		where <math>r</math> is a constant. Some notes on the validity:

	{\| class="sortable" border"=1"		{\| class="sortable" border="1"
	! Case on <math>r</math> !! Values of <math>x</math> for which this makes sense		! Case on <math>r</math> !! Values of <math>x</math> for which this makes sense
	\|-		\|-

Vipul: Created page with "==Statement== We have the following differentiation rule: $\! \frac{d}{dx}(x^r) = rx^{r-1}$ where $r$ is a constant. Some notes on the validity: {| clas..."

2011-12-19T16:34:15Z

Created page with "==Statement== We have the following differentiation rule: <math>\! \frac{d}{dx}(x^r) = rx^{r-1}</math> where <math>r</math> is a constant. Some notes on the validity: {| clas..."

New page

==Statement==

We have the following differentiation rule:

<math>\! \frac{d}{dx}(x^r) = rx^{r-1}</math>

where <math>r</math> is a constant. Some notes on the validity:

{| class="sortable" border"=1"
! Case on <math>r</math> !! Values of <math>x</math> for which this makes sense
|-
| <math>r = 0</math> || all nonzero <math>x</math>. Also makes sense at <math>x = 0</math> if we interpret the right side as 0.
|-
| <math>r</math> a rational number with odd denominator and greater than or equal to 1 || All <math>x</math>
|-
| <math>r</math> a real number greater than 1 that is not rational with odd denominator || All <math>x > 0</math>. One-sided derivative makes sense at 0.
|-
| <math>r</math> a rational number with odd denominator and between 0 and 1 || All <math>x \ne 0</math>. At 0, we have a [[vertical tangent]] or [[vertical cusp]] depending on the numerator of the rational function.
|-
| <math>r</math> a real number between 0 and 1 that is not rational with odd denominator || All <math>x > 0</math>. One-sided vertical tangent at 0.
|-
| <math>r</math> a rational number with odd denominator and less than 0 || All <math>x \ne 0</math>. At 0, we have a [[vertical asymptote]]
|-
| <math>r</math> a real number less than 0 that is not rational with odd denominator || All <math>x > 0</math>. One-sided vertical asymptote at 0.
|}

Differentiation rule for power functions - Revision history

Vipul at 03:14, 26 May 2014

Vipul at 03:13, 26 May 2014

Vipul: /* Statement */

Vipul: Created page with "==Statement== We have the following differentiation rule: \! \frac{d}{dx}(x^r) = rx^{r-1} where r is a constant. Some notes on the validity: {| clas..."

Vipul: Created page with "==Statement== We have the following differentiation rule: $\! \frac{d}{dx}(x^r) = rx^{r-1}$ where $r$ is a constant. Some notes on the validity: {| clas..."