Partial derivatives - How to solve?
Partial derivatives are just like regular derivatives, but for multivariable functions. We’re used to taking the derivative of a single variable function, which is simple because we just take the derivative with respect to the single variable in the function. But with multivariable functions, you’ll need to take a derivative for each variable that exists in your function. So if you have a function in two variables because it’s in terms of x and y, then in order to find the derivative of that function, you’ll actually need to take two partial derivatives, one with respect to x, and the other with respect to y.
In this video you'll learn:
0:28 // What is a derivative and how do you find the derivative at a point?
2:48 // What are partial derivatives?
4:36 // How many partial derivatives will you have?
5:12 // How to find partial derivatives?
5:53 // How to read partial derivatives, and what is the partial derivative symbol called?
10:44 // What are first-order partial derivatives, and what are second-order partial derivatives?
12:37 // How to write second-order partial derivatives?
18:51 // How many second-order partial derivatives will you have?
19:21 // What are mixed partial derivatives?
20:43 // Why are the mixed partial derivatives equal?
24:40 // An example of how to solve for all the partial derivatives
33:10 // How to find the value of the partial derivatives at a particular point
Partial derivatives are just like regular derivatives that you’re used to from Calculus 1, except that they’re for multivariable functions, which you usually get to in Calculus 3.
We’re going to be covering everything about partial derivatives, including what partial derivatives are and when to use them, how to read partial derivative notation (subscription notation and Leibniz notation both), how to calculate partial derivatives, including first order partial derivatives and second order partial derivatives, plus mixed partials. We’ll talk about when and why the mixed second-order partials are always equal to one another.