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I have a function g=f(x,t). The function "g" came from a numerical integration:


and tt(x,r,t) came from a data file.

How to plot the second derivative of g(x,t) with respect to "t" for a fixed "x" using the ND command?

enter image description here

For the first derivative, I can use:

ListPlot[Table[{y, ND[g[y, t], t, 15]}, {y, 50, 200, 3}]]

enter image description here

What about the second derivative? The query "numerical partial derivative" have no answer for the second derivative with respect to the same variable.


marked as duplicate by Jens, bbgodfrey, ciao, m_goldberg, Kuba Apr 23 '15 at 6:08

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  • $\begingroup$ It's been awhile since I took calculus... but I'm pretty sure you can take the derivative with respect to t before you integrate with respect to r, as long as rmin, and rmax don't depend on t, (Leibniz rule?). Then I'd do NIntegrate[D[tt[x,r,t],{t,2}], {r,rmin,rmax}]. $\endgroup$ – N.J.Evans Apr 23 '15 at 1:05
  • $\begingroup$ @N.J.Evans, in fact it is only an example. My function is more complex than the example. $\endgroup$ – Luis Fernando Moura Apr 23 '15 at 15:23
  • 1
    $\begingroup$ You can specify the order of the derivative in the ND function with ND[f[x,y], {x, order}, x0]. $\endgroup$ – N.J.Evans Apr 23 '15 at 17:34

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