Examples of using Partial derivative in English and their translations into Polish
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And we're going to see, it's going to be the same thing here with the partial derivative.
And to solve for psi, we just say, OK, the partial derivative of psi with respect to x is going to be this thing.
using the partial derivative chain rules, is this.
we just took the partial derivative with respect to y.
so it's the partial derivative of the x magnitude with respect to x.
So hopefully this makes some sense just as a review of taking a partial derivative.
You know, if the partial derivative of something in the i-direction, plus the partial derivative, something with respect to y in the j-direction, plus the partial derivative, well, this is if we do it in three dimensions with respect to z in the k-direction.
Let me just show you what the derivative-- using what we knew before you even learned anything about the partial derivative chain rule-- what is the derivative of psi with respect to x?
But when we took the partial derivative of this expression, which we could call M with respect to y,
let's think about what it means to take the partial derivative of this vector valued function with respect to one of the parameters, s or t.
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant as opposed to the total derivative,
This is equal to-- this is the exact same thing as the partial derivative of x with respect to s times i plus the partial derivative y with respect to s times j plus the partial derivative of z with respect to s times k.
with respect to x, and that just falls out of the partial derivative chain rule.
we know that there's some function psi where the partial derivative of psi with respect to x is equal to this expression right here.
So if the derivative, the partial derivative, of this vector field with respect to y is increasing
is an application of his second theorem, which states: If the strain energy of a linearly elastic structure can be expressed as a function of generalised force Qi then the partial derivative of the strain energy with respect to generalised force gives the generalised displacement qi in the direction of Qi.
I would take not a partial derivative, I would take the full derivative of psi with respect to x, it's equal to
you could view this upside down triangle as being equal to the partial derivative with respect to x in the x-direction plus the partial derivative with respect to y in the y-direction,
Well, you would just get the partial derivative of the x dimension with respect to x,
And that's the hardest part about doing these partial derivatives.