# 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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### Infinitesimally small time intervals

When saying that in a small time interval $dt$, the velocity has changed by $d\vec v$, and so the acceleration $\vec a$ is $d\vec v/dt$, are we not assuming that $\vec a$ is constant in that small ...
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### Is every $dm$ piece unequal when using integration of a non-uniformly dense object?

When we want to find the total charge of an object or total mass, usually we start off with a setup such as: $$m = \int dm \:\;\:\text{or} \:\;\:q = \int dq$$ in which we then use (and to keep it ...
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### Why is instantaneous velocity tangent to trajectory?

Trajectory is the path of an object through space as a function of time. However, in many trajectory plots, when the movement is planar, a horizontal position axis and a vertical position axis are ...
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### In Radius of Curvature calculation why do I have to assume $\text{d}^2x/\text{d}t^2=0$?

Recently, I was calculating the radius of curvature of projectile trajectories at certain points. There are two ways to do the same: Given the velocity and acceleration of the particle at some point, ...
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1 vote
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### What is the meaning of $\nabla _{\mu}\nabla _{\nu}\phi(r)$ in general relativity?

I know the covariant derivative of a tensor is $$\nabla_{\mu} V_{\nu}=\partial_\mu V_\nu-\Gamma_{\mu\nu}^{\lambda}V_{\lambda}$$ Now I want to obtain $\nabla_{\mu}\nabla_{\nu}\Phi(x)$ where $\Phi(x)$...
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### What does $\delta/\delta t$-derivative represent in tensor calculus?

Some texts, such as Pavel Grinfeld's, talk about a $\delta/\delta t$-derivative whose role (in trajectory analysis of particles using tensor calculus) is pretty obscure to me. For example, the ...
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### What is the instant velocity? [duplicate]

The velocity is the variation rate of the position correct? So does it make sense to talk about velocity without time?
1 vote
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### Currently self-studying QFT and The Standard Model by Schwartz and I'm stuck at equation 1.5 in Part 1 regarding black-body radiation

So basically the equation is basically a derivation of Planck's radiation law and I can't somehow find any resources as to how he derived it by adding a derivative inside. Planck says that each mode ...
1 vote