Examples of using Partial with respect in English and their translations into Hebrew
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Colloquial
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Ecclesiastic
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Computer
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Programming
And this is the partial, with respect to y.
But if these canceled out, then you would kind of have another partial with respect to x.
This partial with respect to x, that's this.
And then we took the partial, with respect to y.
This partial with respect to y, is this, times y prime.
What happens when we take the partial, with respect to x, and then y?
Take the partial with respect to y, and set that equal to our N expression.
So we said, this is the partial , with respect to x, right?
So i j k, partial with respect to x, partial with respect to y, partial with respect to z.
And then you hold the x constant, and you take the partial, with respect to y.
We take the partial with respect to x, and we get that is equal to 2x plus y.
So the partial of that, with respect to y, so M partial with respect to y, would be 3x plus 2y.
If you take the partial with respect to y, it's 0, because these are constants, from a y point of view.
So we will take the derivative of the first expression with respect to x. mu of x is no longer a constant anymore,since we're taking the partial with respect to x.
So M sub y, or the partial with respect to y, is equal to the partial with respect to x.
I'm kind of taking the derivative with respect to x, and if you could say,and I know you can't, because this partial with respect to y, and the dy, they're two different things.
So it's going to be the partial with respect to y of 0 minus the partial with respect to z of x.
Antiderivative of both sides, and there's some constant h of y-- not constant, there's some function of y-- h ofy that we might have lost when we took the partial with respect to x.
We take a partial with respect to y. x is just a constant, or a function of x can be viewed just as a constant.
So when you take a derivative, when you take a partial with respect to just x, a pure function of just y would get.
If we're taking the partial with respect to y here, mu of x, which is only a function of x, it's not a function of y, it's just a constant term, right?
And of course, this psi is a function of x and y,so when you take the partial with respect to x, when you go that way, you might have lost some function that's only a function of y.
This right here, if we can find a psi, where the partial with respect to x, is this, the partial with respect to y, is this, then this can be rewritten as this.
If you were to take just a partial derivative with respect to x.
The partial of M with respect to y is equal to the partial of N with respect to x.
So the partial of this with respect to y is minus 2x.
Now let's take the partial of this with respect to x.
So if you took the partial derivative with respect to x of this term, you treat a function of y as a constant.
If we were totake the partial of M, with respect to y-- so the partial of psi, with respect to x, is equal to M.
The partial of this with respect to y is equal to the partial of this with respect to N.