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
Derivatives are for measuring how fast functions change. When a function has more dimensions, you need to specify the direction to find the rate of change in that direction.
Imagine a horses saddle, and you’re sitting in the very middle. If you move forward or backward, the surface is getting higher, but when you go to the side, the surface is getting lower. The saddle has 2 dimensions (left/right, forward/backward = x,y), so the partial derivatives describe the slope in each direction: the height of the surface (Z) is a function of how far left/right you are and how far forward or backward you are: Z(x,y), so the slope going left or right is ∂Z/∂x, and the slope going forward or backwards is ∂Z/∂y.
Latest Answers