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