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Re: Simple equation checking..
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