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Re: Creating a function that is a derivative of another function??

• To: mathgroup at smc.vnet.net
• Subject: [mg86737] Re: Creating a function that is a derivative of another function??
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Thu, 20 Mar 2008 02:51:07 -0500 (EST)
• Organization: University of Bergen
• References: <frqpr4$55a$1@smc.vnet.net>

Eric wrote:
> I have a function:
> 
> W[t_] := a*t + b*t^2 + c*t^3
> 
> I want the derivative of this funtion wrt t as another function.  The following seems like it works:
> 
> dW[t_] := D[W[t], t]
> 
> dW[t]
> a + 2 b t + 3 c t^2
> 
> But something isn't right??
> 
> dW[0]
> General::ivar: 0 is not a valid variable. >>
> (output line has a partial derivative symbol, subscript 0 followed by a 0)
> 
> The description of the General::ivar error isn't help either??
> 
> Any idea what's going on here??  How can I assign the derivative of a function as another funtion?!
> 

You need to read this tutorial:

http://reference.wolfram.com/mathematica/tutorial/ImmediateAndDelayedDefinitions.html

The correct solution is
dW[t_] = D[W[t],t]