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Re: Forcing a Derivative
*To*: mathgroup at smc.vnet.net
*Subject*: [mg50767] Re: [mg50753] Forcing a Derivative
*From*: "David Park" <djmp at earthlink.net>
*Date*: Sun, 19 Sep 2004 21:39:23 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
Scott,
You have to actually put the FUNCTION in the Derivative[x][function]
statement and then append a [x] to evaluate at an x value. I assume that you
really want the product of the two functions.
f[x_] = x^2 + 7;
g[x_] = 3x^3 + 23;
Derivative[2][Function[x, f[x]g[x]]]
%[x]
Function[x, 18*x*f[x] + 2*g[x] +
2*Derivative[1][f][x]*Derivative[1][g][x]]
36*x^3 + 18*x*(7 + x^2) + 2*(23 + 3*x^3)
Or using the slot form
Derivative[2][f[#]g[#] &]
%[x]
2*g[#1] + 18*f[#1]*#1 + 2*Derivative[1][f][#1]*
Derivative[1][g][#1] &
36*x^3 + 18*x*(7 + x^2) + 2*(23 + 3*x^3)
This checks with the usual method of taking the derivative.
D[f[x]g[x], {x, 2}]
36*x^3 + 18*x*(7 + x^2) + 2*(23 + 3*x^3)
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: Scott Guthery [mailto:sguthery at mobile-mind.com]
To: mathgroup at smc.vnet.net
How does one force Derivative[n] to actually take the derivative?
For example if ...
f[x_] = x^2 + 7
g[x_]=3x^3 + 23
then
Derivative[2][f * g]
just puts a couple of primes on the product rather than actually computing
the dervative.
Thanks for any insight.
Cheers, Scott
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