Partial Derivatives

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by stephaniejoy19
Last updated 5 years ago

Discipline:
Math
Subject:
Calculus

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Partial Derivatives

Partial Derivatives

So, taking the derivative of fx with respect to x will yield fxx; deriving with respect to y will yield fxy. Taking the derivative of fy with respect to x will yield fyx; deriving with respect to y will yield fyy.Note: A function of 2 variables will have 2 first derivatives and 4 second derivatives; a function of 3 variables will have 3 first derivatives and 9 second derivatives; etc.

The blue line is the partial derivative with respect to x. The gray plane shows us that y is being held constant.

We can also take 2nd Derivatives!Simply derive each partial derivative again.

To learn more about the concept of partial derivatives watch this awesome video: Part 1 is here and Part 2 is here. Also, check out the picture below...it may give you a better idea as well!

But what is a partial derivative...? Like, what does it mean?

Pretty easy, right??You totally got this!Later, you will use this knowledge for lots of other cool stuff, like directional derivatives, tangent planes, and optimization!

Here's how to calculate them!


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