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+--- Thread: derivative of sum gets merged - how to avoid? (/thread-5364.html)
derivative of sum gets merged - how to avoid? - quinyu - 12-19-2015 08:16 PM
Derivative of ((3x-2)^7)/21 + (4-1/(2x^2))^(-1). The result given by HP Prime and the 50g are technically correct but not very neat since they're brought to a common denominator and you cannot do much with it afterwards. Also rather large and difficult to read; and it won't factor out afterwards.
In comparison, TI-nspire CAS delivers (3x-2)^6-(4x)/((8x^2-1)^2), which is much more readable, so does TI-89 Titanium and TI-92. Thomas gives (3x-2)^6-1/((x^3)*(4-1/(2*x^2))^2), so essentially identical, though I don't think I like the form of writing it as a complex fraction. Casio's Classpad II (emu) gives a similarly massive expression as the HPs do.
Mathematica 10 gives the complex fraction form first, and the simple fraction form after a Simplify[]. WolframAlpha gives a single fraction form result. Maple 18 gives a result identical to that of Thomas, and is not easily willing to go to a simple fraction form. Matlab R2015a and MuPAD give the complex fraction too, though with signs swapped in the square. Maxima's output is identical to that of Thomas.
RE: derivative of sum gets merged - how to avoid? - quinyu - 12-20-2015 04:43 AM
A similar case is to be seen when deriving the expression (5-2x)^(-3)+((2/x+1)^4)/8. The results provided by both HP 50g and HP Prime are bulky.
TI-nspire CAS gives 6/(2x-5)^4-(x^3+6x^2+12x+8)/x^5, so it still doesn't play fully nice with the second expression, and inverts the signs for the denominator of the first term (not that it matters), where Thomas gives the form ((2/x+1)^3)/x^2 instead. Same with the TI-89 Titanium and TI-92. The Casio Classpad II (emu) gives a bulky result like the HPs due to the common denominator.
Mathematica delivers the complex fraction form result first, a Simplify[] gives the probably neatest rewrite 6/(5-2x)^4-((2+x)^3)/(x^5); WolframAlpha gives this second one right away. Maxima, Maple, Matlab and MuPAD results are identical to that of Thomas.
RE: derivative of sum gets merged - how to avoid? - Marcus von Cube - 12-20-2015 01:44 PM
I tried with Derive 6. It returns
Code:
4·x 6 5 4 3 2
- ⎯⎯⎯⎯⎯⎯⎯⎯ + 729·x - 2916·x + 4860·x - 4320·x + 2160·x - 576·x + 64
2 2
(8·x - 1)RE: derivative of sum gets merged - how to avoid? - quinyu - 12-20-2015 02:19 PM
That looks a little unpleasant, Mr. von Cube... I do know that some version of Derive is supposed to be the basis of the CAS on the TI-89 and 92. I'm not sure which version and not sure if TI's engineers didn't put their own little tweaks in there afterwards.
RE: derivative of sum gets merged - how to avoid? - parisse - 12-20-2015 02:35 PM
a:=((3x-2)^7)/21 + (4-1/(2x^2))^(-1) followed by a' or diff(a,x) will return a non simplified derivative.
propfrac can be used to take the integer part + a proper fraction if the result has already been rewritten as a single fraction (with the derivative template of the Prime). Unfortunately, there is no EQW on the Prime, you can not factor the denominator of the proper fraction with a few keystrokes.