# Questions tagged [differentials]

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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? ...
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### total differential of a subscripted variable

During use of sub-scripted variables, I came across the following issue Dt[Subscript[x,0]] gives Why is mathematica treating x and not x$_0$ as the ...
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### 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 ...
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### Leave Parts of Formula inactive in partial Differentiation

for thermodynamics, I would like to use a thermodynamic derivative $$\frac 1 T=\frac{\partial S}{\partial E}\Bigg \vert_V$$i.e. the derivative of the entropy S with respect to the energy E with ...
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### 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 ...
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### 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]]; ...
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### Unexplained (possibly faulty) behaviour of Hypergeometric2F1

this might equally be a question for our friends from Math.StackExchange I wanted to verify with Mathematica the analytical ...
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### 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 ...
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### How to program Mathematica to do the differential operator calculation

I want to create a surface Laplacian under the spheroidal coordinates, Now, I already have the surface gradient defined, but I don't know how to find the Laplacian. Since the surface gradient is too ...
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### 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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### Solving algebraic equation system with partial derivatives

I have a list of equations. Some of them are algebraic equations like 2x == y / (y+1), others contains derivatives in them(e.x. ...
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### Symbolic summation with variable bounds and variable number of indices

I wish to compute compute terms like Sum[f[t[j],t[j],...],{j,m},{j,n},...] for arbitrary positive integer n and any ...
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### Proving $d(dx)=d^2x$

Is it possible to carry out the following differential in Mathematica? $$d(dx) = d^2x$$ I tried to write: Dt[1*Dt[x]] the result is: ...
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### 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 <...
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### How does D work with numerical arguments? [duplicate]

If I define f[x_?NumericQ] := (Sow[x]; SawtoothWave[x]) D[f[x], x] /. x -> 1.1 (* 5.29432 *) numeric differentiation fails, despite the function being smooth ...
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### Differentiation and series expansion of dot product - inconsistent results

Bug introduced in 9.0 or earlier and persisting through 11.3 or later If I differentiate a dot product, I get the result I expect D[a.b[x], x] (* a.b'[x] *) ...
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### 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 ...
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### 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 ...