Examples of using Partial derivative in English and their translations into Polish
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So what's the partial derivative?
The partial derivative of 2 with respect to x, well that's 0.
And that is called the partial derivative.
What's the partial derivative of this with respect to x?
It will start taking the partial derivative.
The partial derivative of this inner function with respect to y, it's minus y squared.
Remember this is just the partial derivative operator.
And we're going to see, it's going to be the same thing here with the partial derivative.
So we just calculated the partial derivative at that point.
The partial derivative of f with respect to x-- and still a function of x and y, right?
So this term-- let's see, partial derivative of 0.
Because the partial derivative of a function, purely of y, with respect to x, is going to be 0.
So it will be 2xy plus-- what's the partial derivative of 3y with respect to y?
So if we calculate a partial derivative of our cost function with respect to each of our weights, then we can subtract that value from each weight.
So the divergence of that vector field, is just a partial derivative of this with respect to x.
You just take the partial derivative of the x component with respect to x, and you add that to the partial derivative to the y component with respect to y.
If you were to take just a partial derivative with respect to x.
If you took the derivative of psi with respect to x,it should be equal to this whole thing, just using the partial derivative chain rule.
So let's define the partial derivative of r with respect to s.
We took psi, up here, we treated the functions of x as a constant, andwe just took the partial derivative with respect to y.
So it's equal to the partial derivative with respect to x, of 1/2x.
The partial derivative of the parametrization with respect to one of the parameters crossed with the partial derivative of the parametrization with respect to the other parameter.
And the magnitude is determined by the partial derivative of z with respect to y at that point.
So for example, take the partial derivative of this with respect to x, you're going to get this, right?
Because the derivative of psi, with respect to x,using the partial derivative chain rules, is this.
And then we add that to the partial derivative of the y-component, or the y-function, with respect to y.
And this, hopefully, pops out at you as, gee, we're just taking the partial derivative of each of these functions with respect to s.
All a derivative is, a partial derivative or a normal derivative, it's just a rate of change.
And we need to make sure that we get the order on the cross product right as the partial derivative-- and I'm going to confirm this in a second.
So this is going to be equal to the partial derivative of psi with respect to x plus the partial derivative of psi with respect to y times dy dx.