# 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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### Finding the maximum electric field strength above a ring with a hole in the middle

I'm doing a problem (not homework, by the way) which asks for the electric field strength on the axis of symmetry a distance $x$ above the centre of a circular disc, which has uniform surface charge ...
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### Intuitive Definition of Curl and Stokes' Theorem

I am asking this question on SE Physics because it's about an intuitive derivation, not a rigorously made proof of a theorem. Reading Mathematical Methods for Physics and Engineering by Riley, et al. (...
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### Is there any difference in superscript and subscript notation in finite difference method

Is there any difference in superscript and subscript notation in the finite difference method? I see the same paper use (superscript for $x$ and superscript for $y$ notation) and (subscript for x and ...
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### Do partial derivation respect to velocity and total derivation respect to time commute? [duplicate]

Imagine we have a function of position $x^i$ and velocity $v^i$ $f(x,v)$. Position and velocity are both functions of time $t$. If the function doesn't depend explicitely on time, then we have the ...
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### Generalization of straight line motion under constant acceleration

My question is that, we all know the three equations of straight line motion under constant acceleration, \begin{align} x & =x_{\rm o}+v_{\rm o}\,t+\tfrac12 \mathrm a\,t^2 \tag{1d-a}\label{1d-a}\\ ...
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### Defining the exterior derivative with torsion [duplicate]

As introduced in most standard GR textbooks, the exterior derivative of a p-form $X$ is defined in a coordinate basis as $(dX)_{\mu_1....\mu_{{p+1}}}:= (p+1) \partial_{[\mu_1}X_{\mu_2....\mu_{{p+1}]}}$...
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### Expressing acceleration in terms of velocity and derivative of velocity with respect to position

we know that $$a = \dfrac{dv}{dt}$$ dividing numerator and denominator by $dx$, we get $$a=v\dfrac{dv}{dx}$$ provided that $dx$ is not equal to zero or instantaneous velocity not equal to zero when I ...
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1answer
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### Second derivative of a function in a manifold [closed]

Suppose we have a function curve $\gamma(t)$ on a manifold $M$ . Define the function $$f(t)=\frac{1}{2}g_{ab}\dot\gamma(t)^a\dot\gamma(t)^b$$ Introducing coordinates $x^i$ the first derivative of the ...
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### Derivative with respect to vector of a function depending on vectors

I've been trying to understand this concept for hours without any success. I found similar questions on this forum (Derivative with respect to a vector is a gradient?) but I still don't understand. ...