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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