• Startseite
• Inhalt
• Index

Partial Derivative

Partial Derivative

In calculus the one-variable derivation is not enough. As matheticians are, they want to derive more than one variable in a function. This sounds difficult, but that is a prejudice. In multi-variable calculus you can derive the single variable as you are accostumed to.

In this chapter we derive the function . The rate of change can be described at the particular point: the derivative of f with respective to x. And you have expected it, the derivative of f respective to y.

They are called partial derivatives. The sign for it:  which looks like a cursive d.

and

Procedure: You take derivative of a function of f with respect to x while you treat y as a constant. Then you take derivative of f with respect to y, while in this case you treat x as a constant.

  Example

Find the partial derivatives  and  for the function

Derive first the x and treat y to be constant:

Then derive the y and treat x to be constant:

Remember: The paradigma is