# Questions tagged [differentiation]

Differentiation is the set of techniques and results from Differential Calculus, concerning the calculation of derivatives of functions or distributions.

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### Partial derivatives and Galilean transforms

I have trouble understanding the following: \begin{equation} \frac{\partial}{\partial x'} = \frac {\partial x}{\partial x'} \frac{\partial}{\partial x} + \frac{\partial t}{\partial x'} \frac{\partial}...
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### Partial derivatives in a $PVT$ system

So, I have been studying thermodynamics for a while and some mathematical steps involving partial derivatives have now started to hurt my head. First of all, I understand that whenever we take a $PVT$ ...
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### An identity between the d'Alembertian and the covariant derivative

Suppose $f$ is function which depends on $\phi$, $f = f(\phi)$; and $\phi$ is a scalar field. We define $$\square \equiv g^{\mu\nu} \nabla_\mu \nabla_\nu$$ and $$\nabla_\mu f(\phi) \equiv f_{;\nu}$$ ...
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### Covariant derivatives in a rank 2 tensor

I was trying to prove that for any second order tensor: $$A^{\mu\nu}_{;\mu\nu}=A^{\mu\nu}_{;\nu\mu}$$ considering the torsion free property and locally flat coordinates. Considering the point where ...
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### Is $d \mathbf v · d \mathbf v = d \mathit v^2$?

My teacher has proved the following: $$\mathit v^2 = \mathbf v·\mathbf v = \frac{d\mathbf r}{dt}·\frac{d\mathbf r}{dt} = \left(\frac {ds}{dt}\right)^2 \Rightarrow \mathit v = \frac{ds}{dt}$$ Because ...
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### What is $D$ or $D$-with-a-slash-through-it in the Standard Model equation(s)?

In the mathematical formulation of the Standard Model, which I do not understand yet, there is a capital letter $D$ or $D$-with-a-slash-through-it that I can't find an explanation for. Flip Tanedo (a ...
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### Differential form of Gauss's law from Coulomb's law in spherical coordinates [duplicate]

Coulomb's law for the static electric field of a point charge is given by $$\overrightarrow{E}=\frac{1}{4\pi\epsilon_0}\frac{q}{r^2}\hat{r}$$ Now if we take the divergence of both sides of the above ...
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### What does “Just before” and “Just after” really mean in physics problems?

So I'm stuck in a dynamics problem that asks what is the acceleration of a body just after A, where A is the point that separates the motion of the body from a curvilinear path to projectile motion. ...
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### I need the derivative for this equation [closed]

I want to differentiate this Area equation.
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### What does $d$ stand for in this formula?

Context: I am building a tennis ball machine and am having trouble interpreting the following formula for the flight path of the ball. I know all of the other values in the formula but the source I am ...
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### How a 'variation' $\delta x$ of an independent parameter differs from $dx$? [closed]

I have been reading the Classical Field theory part from The Quantum field theory book of Lewis H Ryder. After defining classical field $\phi(x^\mu)$ he says something about adding variations on both ...
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### Alternative formula for the affine connection in a new coordinate basis

In Hobsons's General Relativity: An Introduction for Physicists, pg. 64, he gave two different expressions for the affine connection $\Gamma'^a_{bc}$ in a transformed coordinate basis $x'^a$ (the ...
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### How is d'Alembertian operator is defined in differential geometry?

Which general formula for the box operator is correct, $\Box=g^{ij}\partial_i\partial_j$ or $\Box=\frac{1}{\sqrt{g}}\partial_i(\sqrt{g}g^{ij}\partial_j)$? I have seen both the definition being used ...
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### Invariance of differential operators

How do we prove that del operator is invariant under any kind of change of coordinates, specifically under galilean transformations? I am getting an extra term containing the relative velocity of two ...
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