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I just finished studying and solving problems for plotting but couldn't figure out this one.

The function $f(x) = x^3+Power[x, (3)^-1]$ for the function itself and it's first three derivatives,plot the graph as shown in the picture according to user given start and finish values.

enter image description here

Note:Arguements for plot; PlotTheme->"Scientific",PlotLabel->"Graph of the function f(x)=x3+x1/3"]

I tried Plot[Evaluate[f[x],{x,1,4}], {x, start, stop}, PlotTheme -> "Scientific", PlotLabel -> "f(x)=x3+x1/3 Functions Graph"] ,giving user entered values as 0 and 10.

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  • $\begingroup$ Alright I made it! Plot[{f[x], f'[x], f''[x], D[f[x], {x, 3}]}, {x, basla, bit}, PlotTheme -> "Scientific", PlotLabel -> "f(x)=x3+x1/3 Fonksiyonunun Grafiği"] but it's still giving a lot of errors lol. $\endgroup$
    – Harvey
    Jan 23, 2017 at 20:25
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    $\begingroup$ You could use f'''[x] for the third derivative. $\endgroup$ Jan 23, 2017 at 21:06

2 Answers 2

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Try the following:

Clear[f]
f[x_] := x^3 + x^(1/3)

Plot[
  Evaluate@Table[D[f[x], {x, i}], {i, 0, 3}], {x, 1, 10},
  PlotLegends -> "Expressions", PlotTheme -> "Scientific",
  PlotLabel -> "f(x)=x^3+ x^(1/3) function and derivatives\n"
]

Mathematica graphics

The main difference in my opinion is the use of Evaluate in the Plot expression, which forces symbolic evaluation of the derivatives and generation of a simple table of functions. This is necessary because of the Hold attributes of the plotting functions.

The function and derivative list are also generated automatically using a Table expression, which keeps the code tidier, at least in my view.

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This is a slight variation on @MarcoB's answer using Tooltip

f[x_] = x^3 + x^(1/3);

Plot[
 Evaluate[Tooltip /@
   {f[x], f'[x], f''[x], f'''[x]}],
 {x, 0, 10},
 Frame -> True,
 Axes -> False,
 PlotRange -> {-40, 620},
 PlotLabel -> ToString[
    HoldForm[f[x]] == f[x], TraditionalForm] <>
   " Fonksiyonunun Grafiği",
 PlotLegends -> {"f(x)", "f'(x)", "f''(x)", "f'''(x)"}]

enter image description here

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