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Re: Simple equation checking..

• To: mathgroup at smc.vnet.net
• Subject: [mg25669] Re: [mg25625] Simple equation checking..
• From: BobHanlon at aol.com
• Date: Wed, 18 Oct 2000 02:52:37 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

In a message dated 10/16/2000 3:52:14 AM, ian at v-wave.com writes:

>I am looking for a way to check equations, for example, the derivative
>of
>((x^3 - 4x + 3)/x^(4/3) is (5x^(10/3) - 8x^(7/3) - 12x^(1/3))/(3x^(8/3))
>when calculated via hand but is (3x^2 - 4)/x^(4/3) - 4(x^3 - 4x +
>3)/(3x^(7/3)) when put through mathematica. What I would like to do is
>if
>there is any way to equate the two and see if the statement is true because
>obviously it can look like two completely different answers (to a student)
>when they are in fact the same.
>
>Another example would be, is there any way to check if E^(:ii:Pi) = -1
>was
>true (at least according to the Euler-Moivre equation), using Mathematica?
>

func = (x^3 - 4x + 3)/x^(4/3);

deriv = D[func, x]

(-4 + 3*x^2)/x^(4/3) - (4*(3 - 4*x + x^3))/(3*x^(7/3))

deriv // Simplify

(-12 + 4*x + 5*x^3)/(3*x^(7/3))

n = Numerator[func];

d = Denominator[func];

manDeriv = (d*D[n, x] - n*D[d,  x])/d^2

(x^(4/3)*(-4 + 3*x^2) - 4/3*x^(1/3)*(3 - 4*x + x^3))/x^(8/3)

manDeriv // Simplify

(-12 + 4*x + 5*x^3)/(3*x^(7/3))

(manDeriv == deriv) // Simplify

True

Sometimes it is necessary to use FullSimplify rather than Simplify. 
However, try Simplify first since FullSimplify can take considerable time.

E^(I*Pi) == -1

True


Bob Hanlon