What exactly is a partial derivative? I have a basic idea of a derivative i.e, I know that dy/dx is rate of change of y with respect to x and that it represents the slope of a curve
Thanks!
In: Mathematics
So in a regular derivative, you just have one variable. For example, Y=2X. X is the only variable in this equation, so the only way Y can change is if X changes. So the only possible rate of change that you can calculate is dy/dx.
In a partial derivative, it’s exactly the same thing as a regular derivative except now your equation is a function of more than 1 variable. For example, Y=XZ. There are two variables, X and Z. So, Y can change by two ways! If you change X, Y will change. If you change Z, Y will also change. The partial derivative wants to examine how Y changes as only ONE variable changes, and holding the others constant. Basically, we want to see how Y reacts if we ONLY change X OR Z.
So you can calculate two partial derivatives. dy/dx and dy/dz. In dy/dx, it’s saying “how does Y change when X changes, and Z is held constant”. In dy/dz, it’s saying “how does Y change when Z changes, and X is held constant”.
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