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I want to create a computational rule like, $ \frac{\partial}{\partial h_{i}}\int f\left(h_{i}\right)di:=\frac{\partial f\left(h_{i}\right)}{\partial h_{i}}$ . This rule is somehow useful when doing models of heterogeneous agents. To achieve this, I use the code, Unprotect[D] D[Integrate[x_, i_], p_] := D[x, p] /; ! FreeQ[p, i] This works for codes like, D[Integrate[f[h[i]/p a], i], h[i]] which returns,Read more

I have a list of equations. Some of them are algebraic equations like 2x == y / (y+1), others contains derivatives in them(e.x. df/dx == 0). Note they are not differential equations. As they can be simplified from other algebraic equations before taking the (partial) derivative. After taking the partial derivative, they will all beRead more

I want to be able to treat $ z$ and its complex conjugate as independent variables, so that for instance $ \partial (z\bar z)/\partial z = \bar z$ . When I try to do this in Mathematica, via D[z Conjugate[z], z] it returns $ z1$ Conjugate$ ^\prime(z1)+z1^*$ , because it treats $ \bar z$ asRead more

I have a function $ f:\Re^2\to\Re^2$ and would like to understand why $ |Jf(x)|=\max_\theta|D_\theta f(x)|\cdot\min_\theta|D_\theta f(x)|$ , that is, why the determinant of the Jacobian of $ f$ at $ x$ is equal to the product of min and max of the directional derivatives at $ x$ . I think it must be a moreRead more

I am working on a problem that results in expressions with trig functions and their derivatives along with several other functions and derivatives. At one point, the subtraction of two expressions resulted in an expression proportional to 1 + sin”[x] / sin[x] whose value is obviously zero. How do I get Mathematica to evaluate theRead more

so I have an expression called Ex1 and some function Z[r,t], Ex1 = r*D[Z,r] I then define what Z is, Z = r^3 + G[r,t] But when I type Ex1 again, the expression is not simplified. It does not take the derivative of Z. I would like the expression to be evaluated knowing what ZRead more

Draws from Gaussian processes with zero mean and radial basis covariance kernels are smooth almost surely. Is there any work on the distribution of the derivative of a draw from such a GP?Read more

My understanding of how derivations on commutative rings are like derivatives is that a derivation on $ R$ is differentiation with respect to a vector field on $ \text{Spec}(R)$ . But derivations are supposed to be thought of as like derivatives in a wider context than commutative rings, and I don’t really understand how. TakeRead more

(1) f[x1_, x2_, x3_] := x1^100 * x2^200 * x3^300 Derivative[1, 2, 3][f][x1, x2, x3] (2) I want to get the same result as (1) when I have two lists: variables = Table[Subscript[x, i], {i, 1, 3}] variableIndex = Table[i, {i, 1, 3}] Derivative[variableIndex][f][variables] But (2) doesn’t work. What should I do?Read more

I was wondering if it is possible to force particular style of displaying derivatives in Mathematica. For example if I type: $ $ AB\partial_\mu C[\mu]$ $ After execution it automatically be displayed as: $ $ ABC'(\mu)$ $ I would prefer to have my derivatives with $ \partial_\mu$ symbol for reasons. Is this possible?Read more