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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 $$$\frac{\partial}{\partial x}\left(x^{2} - y^{2}\right)$$$

The derivative of a sum/difference is the sum/difference of derivatives:

$${\color{red}{\frac{\partial}{\partial x}\left(x^{2} - y^{2}\right)}}={\color{red}{\left(\frac{\partial}{\partial x}\left(x^{2}\right) - \frac{\partial}{\partial x}\left(y^{2}\right)\right)}}$$

Apply the power rule $$$\frac{\partial}{\partial x} \left(x^{n} \right)=n\cdot x^{-1+n}$$$ with $$$n=2$$$:

$${\color{red}{\frac{\partial}{\partial x}\left(x^{2}\right)}} - \frac{\partial}{\partial x}\left(y^{2}\right)={\color{red}{\left(2 x^{-1 + 2}\right)}} - \frac{\partial}{\partial x}\left(y^{2}\right)=2 x - \frac{\partial}{\partial x}\left(y^{2}\right)$$

The derivative of a constant is 0:

$$2 x - {\color{red}{\frac{\partial}{\partial x}\left(y^{2}\right)}}=2 x - {\color{red}{\left(0\right)}}$$

Thus, $$$\frac{\partial}{\partial x}\left(x^{2} - y^{2}\right)=2 x$$$

Answer: $$$\frac{\partial}{\partial x}\left(x^{2} - y^{2}\right)=2 x$$$


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