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# Derive in a point a

Posted 9 years ago
 I have this function g(x=(Arctan(x)^2+arcsin(x/2) I want f'(1) when i derive i get for hand i get the same result as mathematica so correct when i put 1 in f'(x) I get (pi/4)/2+(pi/2)/sqrt(1/4)=pi/2 + pi=3pi/2 i want to check if this is correct if i have function f(x)=3x+1 f(1)=3*1+1=4 how do i put in the value 1 in mathematica for my function? or how do i derive a function in a point so the result will be a number? of course, i can save the derivietive as a function and then put in my value for x also cant find how i do that :( Thanks in advance /Peter
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Posted 9 years ago
 And this: g[x_] := ArcTan[x]^2 + ArcSin[x/2]; dg[x_] = D[g[x], x]; p1 = Plot[{g[x], dg[x]}, {x, -2, 2}, PlotLegends -> "Expressions", Epilog -> {PointSize[0.02], Point[{1, g}]}] In:= (* dg[x_]= was used rather than dg[x_]:= because we want the \ right hand side evaluated before the rule is defined. Look up Set and \ SetDelayed. *) In:= (* = would work here as well, but := is used more often *) f[x_] := 3 x + 1; (* defines a function *) In:= f[a] (* evaluates it at a *) Out= 1 + 3 a In:= f Out= 4 
Posted 9 years ago
 This? In:= D[ArcTan[x]^2 + ArcSin[x/2], x] Out= 1/(2 Sqrt[1 - x^2/4]) + (2 ArcTan[x])/(1 + x^2) In:= % /. x -> 1 Out= 1/Sqrt + \[Pi]/4