Lösung 1.2:2a

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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,


\displaystyle \sin \left\{ \left. {} \right\} \right.


and then an inner part, \displaystyle \left\{ \left. {} \right\} \right.=x^{2}.

When we differentiate compound expressions, we first differentiate the outer part, \displaystyle \sin \left\{ \left. {} \right\} \right., as if \displaystyle \left\{ \left. {} \right\} \right. were the variable that we differentiate with respect to, and then we multiply with the derivative of the inner part \displaystyle \left\{ \left. {} \right\} \right.^{\prime }, so that


\displaystyle \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

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