Lösung 1.2:3e

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At first sight, the expression looks like “
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At first sight, the expression looks like “''e'' raised to something” and therefore we differentiate using the chain rule,
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<math>e</math>
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raised to something” and therefore we differentiate using the chain rule:
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{{Displayed math||<math>\frac{d}{dx}\,e^{\bbox[#FFEEAA;,1.5pt]{\sin x^2}} =
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e^{\bbox[#FFEEAA;,1.5pt]{\sin x^2}}\cdot \bigl( \bbox[#FFEEAA;,1.5pt]{\sin x^2}\bigr)'\,\textrm{.}</math>}}
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<math>\frac{d}{dx}e^{\left\{ \left. \sin x^{2} \right\} \right.}=e^{\left\{ \left. \sin x^{2} \right\} \right.}\centerdot \left( \left\{ \left. \sin x^{2} \right\} \right. \right)^{\prime }</math>
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Then, we differentiate “sine of something”,
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{{Displayed math||<math>\begin{align}
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Then, we differentiate “sine of something”:
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e^{\sin x^2}\cdot \bigl( \sin \bbox[#FFEEAA;,1.5pt]{x^2} \bigr)'
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&= e^{\sin x^2}\cdot \cos\bbox[#FFEEAA;,1.5pt]{x^2} \cdot \bigl( \bbox[#FFEEAA;,1.5pt]{x^2}\bigr)'\\[5pt]
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&= e^{\sin x^2}\cdot \cos x^2\cdot 2x\,\textrm{.}
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<math>\begin{align}
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\end{align}</math>}}
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& e^{\sin x^{2}}\centerdot \left( \left\{ \left. \sin x^{2} \right\} \right. \right)^{\prime }=e^{\sin x^{2}}\centerdot \cos \left\{ \left. x^{2} \right\} \right.\centerdot \left( \left\{ \left. x^{2} \right\} \right. \right)^{\prime } \\
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& =e^{\sin x^{2}}\centerdot \cos x^{2}\centerdot 2x \\
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\end{align}</math>
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Version vom 13:12, 15. Okt. 2008

At first sight, the expression looks like “e raised to something” and therefore we differentiate using the chain rule,

\displaystyle \frac{d}{dx}\,e^{\bbox[#FFEEAA;,1.5pt]{\sin x^2}} =

e^{\bbox[#FFEEAA;,1.5pt]{\sin x^2}}\cdot \bigl( \bbox[#FFEEAA;,1.5pt]{\sin x^2}\bigr)'\,\textrm{.}

Then, we differentiate “sine of something”,

\displaystyle \begin{align}

e^{\sin x^2}\cdot \bigl( \sin \bbox[#FFEEAA;,1.5pt]{x^2} \bigr)' &= e^{\sin x^2}\cdot \cos\bbox[#FFEEAA;,1.5pt]{x^2} \cdot \bigl( \bbox[#FFEEAA;,1.5pt]{x^2}\bigr)'\\[5pt] &= e^{\sin x^2}\cdot \cos x^2\cdot 2x\,\textrm{.} \end{align}

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse2-TU-Berlin/index.php/L%C3%B6sung_1.2:3e“