Sine of square function - Revision history

Vipul: /* Definition */

2011-12-19T19:38:37Z

Definition

← Older revision		Revision as of 19:38, 19 December 2011
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	<math>x \mapsto \sin(x^2)</math>		<math>x \mapsto \sin(x^2)</math>

	Note that this is different from <matH>\sin^2</math>, the [[sine-squared function]].		Note that this is different from <matH>\sin^2</math>, the [[sine-squared function]]. It also differs from the [[sine of sine function]], obtained by composing the sine function with itself.

	==Graph==		==Graph==

Vipul: /* Using the chain rule for differentiation */

2011-12-19T19:37:51Z

Using the chain rule for differentiation

← Older revision		Revision as of 19:37, 19 December 2011
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	===Using the chain rule for differentiation===		===Using the chain rule for differentiation===

			{{quotation\|'''WHAT WE USE''': [[chain rule for differentiation]], [[differentiation rule for power functions]], [[sine function#Differentiation]]}}

	<section begin="differentiation"/>		<section begin="differentiation"/>

Vipul at 00:38, 28 November 2011

2011-11-28T00:38:54Z

← Older revision		Revision as of 00:38, 28 November 2011
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	[[File:Sineofsquarebasic.png\|600px]]		[[File:Sineofsquarebasic.png\|600px]]

			==Differentiation==

			===Using the chain rule for differentiation===

			<section begin="differentiation"/>

			We use the [[chain rule for differentiation]] viewing the function as the composite of the [[square function]] on the inside and the [[sine function]] on the outside:

			<math>\frac{d}{dx}[\sin(x^2)] = \frac{d(\sin(x^2))}{d(x^2)} \frac{d(x^2)}{dx} = (\cos(x^2))(2x) = 2x\cos(x^2)</math>

			<section end="differentiation"/>

Vipul: Created page with "{{particular function}} {{angular function radian convention}} ==Definition== This function is defined as the composite of t..."

2011-09-04T13:44:56Z

Created page with "{{particular function}} {{angular function radian convention}} ==Definition== This function is defined as the composite of t..."

New page

{{particular function}}
{{angular function radian convention}}

==Definition==

This function is defined as the [[defining ingredient::composite of two functions|composite]] of the [[defining ingredient::sine function]] and the [[defining ingredient::square function]]. Explicitly, it is the function:

<math>x \mapsto \sin(x^2)</math>

Note that this is different from <matH>\sin^2</math>, the [[sine-squared function]].

==Graph==

Here is a zoomed out graph for the domain restricted to <math>[-5\sqrt{\pi},5\sqrt{\pi}]</math>:

[[File:Sineofsquarebasic.png|600px]]