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Научный форум dxdyМатематика, Физика, Computer Science, Machine Learning, LaTeX, Механика и Техника, Химия,Биология и Медицина, Экономика и Финансовая Математика, Гуманитарные науки |
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Научный форум dxdyМатематика, Физика, Computer Science, Machine Learning, LaTeX, Механика и Техника, Химия,Биология и Медицина, Экономика и Финансовая Математика, Гуманитарные науки |
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| Страница 1 из 3 |
[ Сообщений: 42 ] | На страницу 1, 2, 3 След. |
17.11.2012, 20:56 
![$\[y = x^3 + e^{xy}\]$](https://dxdy-03.korotkov.co.uk/f/6/0/3/603fa79ae915f317838a633ad78dfc6082.png "$\[y = x^3 + e^{xy}\]$")
![$\[
\begin{gathered}
y' = 3x^2 + e^{xy} \cdot \left( {y' \cdot x + x' \cdot y} \right) = 3x^2 + e^{xy} \cdot y' \cdot x \hfill \\
y' - y' \cdot e^{xy} \cdot x = 3x^2 \hfill \\
y' = \frac{{3x^2 }}
{{1 - e^{xy} \cdot x}} \hfill \\
y'' = \frac{{6xy \cdot (1 - e^{xy} \cdot x) - y \cdot \left( {1 - e^{xy} \cdot x} \right)'}}
{{(1 - e^{xy} \cdot x)^2 }} \hfill \\
\end{gathered}
\]
$](https://dxdy-02.korotkov.co.uk/f/d/d/a/dda015c20fec996a72cd89b737a6bc0982.png "$\[
\begin{gathered}
y' = 3x^2 + e^{xy} \cdot \left( {y' \cdot x + x' \cdot y} \right) = 3x^2 + e^{xy} \cdot y' \cdot x \hfill \\
y' - y' \cdot e^{xy} \cdot x = 3x^2 \hfill \\
y' = \frac{{3x^2 }}
{{1 - e^{xy} \cdot x}} \hfill \\
y'' = \frac{{6xy \cdot (1 - e^{xy} \cdot x) - y \cdot \left( {1 - e^{xy} \cdot x} \right)'}}
{{(1 - e^{xy} \cdot x)^2 }} \hfill \\
\end{gathered}
\]
$")
![$
\[
\begin{gathered}
y' = 3x^2 + e^{xy} \cdot \left( {y' \cdot x + x' \cdot y} \right) = 3x^2 + e^{xy} \cdot y' \cdot x + y \cdot e^{xy} \hfill \\
y' = \frac{{y \cdot e^{xy} + 3x^2 }}
{{1 - x \cdot e^{xy} }} \hfill \\
\end{gathered}
\]
$](https://dxdy-01.korotkov.co.uk/f/c/2/2/c22efb72c13c15354679975d915d5aa382.png "$
\[
\begin{gathered}
y' = 3x^2 + e^{xy} \cdot \left( {y' \cdot x + x' \cdot y} \right) = 3x^2 + e^{xy} \cdot y' \cdot x + y \cdot e^{xy} \hfill \\
y' = \frac{{y \cdot e^{xy} + 3x^2 }}
{{1 - x \cdot e^{xy} }} \hfill \\
\end{gathered}
\]
$")
![$\[y' = \frac{{y \cdot e^{xy} + 6x}}{{1 - x \cdot e^{xy} }}\]$](https://dxdy-03.korotkov.co.uk/f/e/6/5/e658e1c7107ca55de786e74957c50b5382.png "$\[y' = \frac{{y \cdot e^{xy} + 6x}}{{1 - x \cdot e^{xy} }}\]$")
![$\[y'' = \frac{{(y \cdot e^{xy} + 6x)' \cdot \left( {1 - x \cdot e^{xy} } \right) - \left( {1 - x \cdot e^{xy} } \right)' \cdot \left( {y \cdot e^{xy} + 6x} \right)}}
{{\left( {1 - x \cdot e^{xy} } \right)^2 }}\]$](https://dxdy-04.korotkov.co.uk/f/f/c/6/fc6a0efbbc772e5549097da9ca69073c82.png "$\[y'' = \frac{{(y \cdot e^{xy} + 6x)' \cdot \left( {1 - x \cdot e^{xy} } \right) - \left( {1 - x \cdot e^{xy} } \right)' \cdot \left( {y \cdot e^{xy} + 6x} \right)}}
{{\left( {1 - x \cdot e^{xy} } \right)^2 }}\]$")
![$\[\begin{gathered} y' = \frac{{y \cdot e^{xy} + 3x^2 }}{{1 - x \cdot e^{xy} }} \hfill \\ t = e^{xy} \hfill \\ y' = \frac{{3x^2 + y \cdot t}}{{1 - x \cdot t}} \hfill \\ \end{gathered} \]$](https://dxdy-02.korotkov.co.uk/f/1/e/d/1edd9758097b6e100a388e666b0c2b0882.png "$\[\begin{gathered} y' = \frac{{y \cdot e^{xy} + 3x^2 }}{{1 - x \cdot e^{xy} }} \hfill \\ t = e^{xy} \hfill \\ y' = \frac{{3x^2 + y \cdot t}}{{1 - x \cdot t}} \hfill \\ \end{gathered} \]$")
