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Re: What is the difference between z[x_]:= D[y[x],x] and z[x_]:=y'[x]?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg27458] Re: What is the difference between z[x_]:= D[y[x],x] and z[x_]:=y'[x]?
*From*: "Paul Lutus" <nospam at nosite.com>
*Date*: Mon, 26 Feb 2001 01:29:24 -0500 (EST)
*References*: <97cdfc$d6m@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
"liwen liwen" <gzgear at yahoo.com> wrote in message
news:97cdfc$d6m at smc.vnet.net...
> Dear friends,
> How are you!
> I want to know the difference between z[x_]:=
> D[y[x],x] and z[x_]:=y'[x].
There is no difference.
In[1]:= y'[x] == D[y[x],x]
Out[1]= True
> Also,I want to why I can not find the answer for the
> u[0.5] by the following routine:
>
> (r1[t_] = 93/(1 + 0.12*Cos[3*t]);
> d1[t_] := ArcTan[r1[t]/D[r1[t], t]];
> Block[{t}, u[t_] := If[(Pi/3 >= t > 0), d1[t]]];
> )
>
> u[0.5]
> General::"ivar": "\!\(0.5`\) is not a valid variable."
>
> But it is available by the following routine:
>
> (r1[t_] = 93/(1 + 0.12*Cos[3*t]);
> d1[t_] = ArcTan[r1[t]/D[r1[t], t]];
> Block[{t}, u[t_] := If[(Pi/3 >= t > 0), d1[t]]];
> )
>
> u[0.5]
> 1.22872
r1[t_] := 93/(1 + 0.12*Cos[3*t]);
d1[t_] := ArcTan[r1[t]/r1'[t]];
Block[{t}, u[t_] := If[(Pi/3 >= t > 0), d1[t]]];
--
Paul Lutus
www.arachnoid.com
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