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Lösung 1.2:2a

Aus Online Mathematik Brückenkurs 2

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K (Lösning 1.2:2a moved to Solution 1.2:2a: Robot: moved page)
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The expression is composed of two parts: first, an outer part,
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<center> [[Image:1_2_2a.gif]] </center>
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<math>\sin \left\{ \left. {} \right\} \right.</math>
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and then an inner part,
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<math>\left\{ \left. {} \right\} \right.=x^{2}</math>.
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When we differentiate compound expressions, we first differentiate the outer part,
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<math>\sin \left\{ \left. {} \right\} \right.</math>, as if
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<math>\left\{ \left. {} \right\} \right.</math>
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were the variable that we differentiate with respect to, and then we multiply with the derivative of the inner part
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<math>\left\{ \left. {} \right\} \right.^{\prime }</math>, so that
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<math>\frac{d}{dx}\sin \left\{ \left. x^{2} \right\} \right.=\cos \left\{ \left. x^{2} \right\} \right.\centerdot \left( \left\{ \left. x^{2} \right\} \right. \right)^{\prime }=\cos x^{2}\centerdot 2x</math>

Version vom 12:46, 11. Okt. 2008

The expression is composed of two parts: first, an outer part,


sin


and then an inner part, =x2.

When we differentiate compound expressions, we first differentiate the outer part, sin, as if were the variable that we differentiate with respect to, and then we multiply with the derivative of the inner part , so that


ddxsinx2=cosx2x2=cosx22x 

Von „http://wiki.math.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_1.2:2a“