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Questions tagged [differentials]

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239 views

Differentiation and series expansion of dot product - inconsistent results

Bug introduced in 9.0 or earlier and persisting through 11.3 or later Bug resolved in 12.0 As of 12.0, we have an unevaluated result - inconsistent with the differentiation result, but not invalid. ...
422 views

Can we abuse notation and write equations in differential one-form?

Consider a simple equation with a one-form on both sides (mathworld.wolfram is also aware of this): $$y\mathrm{d}x = \mathrm{d}y$$ This is a perfectly valid abuse of notation. We can carry the $y$ ...
341 views

Bug? Problem with derivative of interpolating function from FEM

Bug introduced in 10 or earlier and fixed in version 10.4 I am really not sure if this is a bug or I am missing something very trivial. QUESTION: What I am missing in order to obtain the partial ...
148 views

Chain rule when taking derivatives with UpValues

I have a summation function, for which I have defined derivation via Customsum /: D[Customsum[idx_, a_, b_, exprs_], y_] := Custom`sum[idx, a, b D[expr, y]]; ...
298 views

Better replacement rules to perform this change of variables?

In cosmology, it is common to work with both a normal time variable t and a “conformal” time variable τ, which is defined such ...
1k views

Taking the derivative of a function with indexed variables

I have a number of functions that depend on a variable x. I am using a second, integer variable to index these functions, i.e. something like ...
542 views

How best to write an exponential of differential operators?

I want to evaluate a term like this, $$\left.\exp\left({1\over 2}\sum_{i,j=1}^{n}(A^{-1})_{ij}{\partial \over \partial x_i}{\partial \over \partial x_j}\right) f(\vec{x})\right|_{\vec{x}=0}$$ and I ...
731 views

Mathematica package for supergravity and superstring theory

I am looking for a Mathematica package that can manipulate tensors for supergravity, string theory or M-theory. I am particularly looking for a package that can do spinor and Clifford algebra ...
125 views

Apparently contradictory output from Series and D

I defined a function as: g[b_] := Integrate[f[n]Exp[-b DA (n.u)^2], n] Obviously D[g[b], b] /. b -> 0 gives ...
162 views

Find $\frac{dy}{dx}$ if $x\sqrt{1+y}+y\sqrt{1+x}=0$

Find $\frac{dy}{dx}$ if $x\sqrt{1+y}+y\sqrt{1+x}=0$ for $-1\leq x\leq 1$ $$\frac{dy}{dx}=\frac{-1}{(1+x)^2}\text{ if }x\neq y$$ If it was like $y=\sqrt{1+x}$ i think i know how to do it ...
650 views

How to define a differential operator in Mathematica? [duplicate]

I want to define an operator $(\partial_{t}+1)^{2}=\partial_{t}\partial_{t}+2\partial_{t}+1$. Then, I want it to act on $t$. My code looks like this: ...
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How to differentiate a function that is a function of other functions?

I am trying to differentiate the function epsilon1 with respect to u, but why this does not give me any output? ...
111 views

4k views

Find dy/dx given an equation

Here's a homework problem from the Coursera course Calculus: Single Variable by Robert Ghrist Find the derivative $\frac{dy}{dx}$ from the equation $x \tan y - y^2 \ln x=4$ I wanted to check my ...
348 views

Derivative of a plot [closed]

I plotted a graph numerically, so I don't have a definition of the plotted function. Now I want to plot the derivative of this graph. Is there any way to do it in Mathematica? I have the following ...
246 views

Does Mathematica understand the concept of infinitesimal increment?

Commonly, in textbooks, differential of differential increment vanishes, good example is how Euler-Lagrange equations are derived using the differential (from step 2 to step 3 here, you can see ...
83 views

Specifying independence of a variable in a function

I am dealing with a function of a finite number of variables and among the operations I wish to do is to differentiate it repeatedly with respect with any of the variables. Now this function happens ...
637 views

Differential equation solution

DSolve[y''[x] + (a - (b*x^2 - c)*x^2)*y[x] == 0, y[x], x] I couldn't solve this equation, please help
422 views

How to compute the composition of linear differential operator [duplicate]

For example, I have to write down the differential operator below as a polynomial in $\partial$ $$(\partial-f_n(x))(\partial-f_{n-1}(x))\cdots(\partial-f_1(x))$$where the product the the composition. ...
2k views

Solve a total derivative - independent vs. dependent variables

I am trying to force mathematica to solve a generally defined function for d lp: In a reduced version, w depends on l2, ...
74 views

How to define a variable to be a function of all the arguments but one?

I have several variables (coordinates) $x_1, x_2, x_3, x_4, z$ and a lot (21, to be precise) functions $g_i$ which are assumed to depend on $x_1, x_2,x_3, x_4$, but not on $z$. I also have a ...
48 views

Differentiating nested functions, Differentiate unevaluated function

I have two functions G[x_]:=x^6; S[x_]:=G[x]+x^12 I would like to operate on S[x] with respect to x in three ways, where we take the differentiation as ...
53 views

Differentiate an Integral-Assumption needed

I already looked into the smaller problems, but I just don't get the clean first derivative, because Mathematica wants to work with imaginary numbers. How do I best supress this here? I tried it with <...
160 views

Differentiation of Vector Equation [closed]

Is it possible to get symbolic derivatives of equations with vectors as arguments without specifying every vector element explicitly. Something like ...
49 views

95 views

Unable to configure a system of differential equations [closed]

My differential equations have been written as ...
159 views

Using Derivative with list in curly brackets

I'd like to make a formula for a sum containing Derivative where the number of arguments in the latter depends on an input parameter n. Also involved is a list <...
Let $f:\mathbb{R}_+\rightarrow \mathbb{R}$ be a function differentiable for $x>0$ but non differentiable at $x=0$ (for instance $f=\sqrt{\cdot}$) and $g$ be a polynomial function. I know how to ...
I am solving the following system of equations with Mathematica. $u'=-k_{1}ux+k_{2}x^2, x'=k_{1}ux-k_{2}x^2$ and I obtain the solution for x: \$x(t)=\frac{e^{k_{1}C_{1}(t+C_{2})}k_{1}C_{1}}{-1+e^{k_{1}...