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Rechner für partielle Ableitungen

Partielle Ableitungen Schritt für Schritt berechnen

Dieser Online-Rechner berechnet die partielle Ableitung der Funktion, wobei die Schritte angezeigt werden. Sie können eine beliebige Reihenfolge der Integration angeben.

Solution

Your input: find $\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(3 x + 4 y\right)$

First, find $\frac{\partial}{\partial l}\left(3 x + 4 y\right)$

The derivative of a constant is 0:

${\color{red}{\frac{\partial}{\partial l}\left(3 x + 4 y\right)}}={\color{red}{\left(0\right)}}$

Thus, $\frac{\partial}{\partial l}\left(3 x + 4 y\right)=0$

Next, $\frac{\partial^{2}}{\partial l \partial a}\left(3 x + 4 y\right)=\frac{\partial}{\partial a} \left(\frac{\partial}{\partial l}\left(3 x + 4 y\right) \right)=\frac{\partial}{\partial a}\left(0\right)$

The derivative of a constant is 0:

${\color{red}{\frac{\partial}{\partial a}\left(0\right)}}={\color{red}{\left(0\right)}}$

Thus, $\frac{\partial}{\partial a}\left(0\right)=0$

Next, $\frac{\partial^{3}}{\partial l \partial a \partial m}\left(3 x + 4 y\right)=\frac{\partial}{\partial m} \left(\frac{\partial^{2}}{\partial l \partial a}\left(3 x + 4 y\right) \right)=\frac{\partial}{\partial m}\left(0\right)$

The derivative of a constant is 0:

${\color{red}{\frac{\partial}{\partial m}\left(0\right)}}={\color{red}{\left(0\right)}}$

Thus, $\frac{\partial}{\partial m}\left(0\right)=0$

Next, $\frac{\partial^{4}}{\partial l \partial a \partial m \partial d}\left(3 x + 4 y\right)=\frac{\partial}{\partial d} \left(\frac{\partial^{3}}{\partial l \partial a \partial m}\left(3 x + 4 y\right) \right)=\frac{\partial}{\partial d}\left(0\right)$

The derivative of a constant is 0:

${\color{red}{\frac{\partial}{\partial d}\left(0\right)}}={\color{red}{\left(0\right)}}$

Thus, $\frac{\partial}{\partial d}\left(0\right)=0$

Next, $\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(3 x + 4 y\right)=\frac{\partial}{\partial a} \left(\frac{\partial^{4}}{\partial l \partial a \partial m \partial d}\left(3 x + 4 y\right) \right)=\frac{\partial}{\partial a}\left(0\right)$

The derivative of a constant is 0:

${\color{red}{\frac{\partial}{\partial a}\left(0\right)}}={\color{red}{\left(0\right)}}$

Thus, $\frac{\partial}{\partial a}\left(0\right)=0$

Therefore, $\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(3 x + 4 y\right)=0$

Answer: $\frac{\partial^{5}}{\partial l \partial a \partial m \partial d \partial a}\left(3 x + 4 y\right)=0$