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  2. Rechner
  3. Rechner: Analysis III
  4. Analysis-Rechner

Rechner für partielle Ableitungen

Partielle Ableitungen Schritt für Schritt berechnen

Dieser Online-Rechner berechnet die partielle Ableitung der Funktion und zeigt die Rechenschritte an. Sie können jede Ableitungsordnung angeben.

Enter a function:

Enter the order of integration:

Hint: type x^2,y to calculate `(partial^3 f)/(partial x^2 partial y)`, or enter x,y^2,x to find `(partial^4 f)/(partial x partial y^2 partial x)`.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please contact us.

Solution

Your input: find $$$\frac{\partial}{\partial y}\left(x y\right)$$$

Apply the constant multiple rule $$$\frac{\partial}{\partial y} \left(c \cdot f \right)=c \cdot \frac{\partial}{\partial y} \left(f \right)$$$ with $$$c=x$$$ and $$$f=y$$$:

$${\color{red}{\frac{\partial}{\partial y}\left(x y\right)}}={\color{red}{x \frac{\partial}{\partial y}\left(y\right)}}$$

Apply the power rule $$$\frac{\partial}{\partial y} \left(y^{n} \right)=n\cdot y^{-1+n}$$$ with $$$n=1$$$, in other words $$$\frac{\partial}{\partial y} \left(y \right)=1$$$:

$$x {\color{red}{\frac{\partial}{\partial y}\left(y\right)}}=x {\color{red}{1}}$$

Thus, $$$\frac{\partial}{\partial y}\left(x y\right)=x$$$

Answer: $$$\frac{\partial}{\partial y}\left(x y\right)=x$$$


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