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

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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