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I'm currently practicing differentiation. The exercise I currently have is the following

Find the derivative of:

$(x + 6)^3 (9 x^3 - 2)^5$

Okay, well I can do that now. When I do this I uses the chain/product rule to get the following result:

$3(x+6)^2 (9x^3 -2)^5 + 45(x+6)^3 (3x^2) (9x^3 - 2)^4$

However, when I put this in wolfram alpha I get the following result (and it matches the answer from my exercise):

$6(x+6)^2 (2-9 x^3)^4 (27 x^3+135 x^2-1)$

I'm staring at this for an hour now, but I don't get how they get rid of the addition, and how they'd get rid of (for example) $(9x^3-2)^5$

1 Answers 1

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I don't know how wolfram alpha's algorithms actually did this, but here's how it could have been done:
$3(x+6)^2(9x^3-2)^5+45(x+6)^3(3x^2)(9x^3-2)^4$
$=3(x+6)^2(9x^3-2)^4(9x^3-2)+3(x+6)^2(9x^3-2)^4(45x^2)(x+6)$
$=3(x+6)^2(9x^3-2)^4((9x^3-2)+45x^2(x+6))$
$=3(x+6)^2(9x^3-2)^4(9x^3-2+45x^3+270x^2)$
$=3(x+6)^2(9x^3-2)^4(54x^3+270x^2-2)$
$=6(x+6)^2(9x^3-2)^4(27x^3+135x^2-1)$

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    @Timo Though your answer is correct, it might not be considered a proper form. Just like it is usually not recommended to leave 15/25 instead of 3/5 as answer. If you are concerned about the test, make sure to clarify it with professor, since some would mark such an answer down.2011-01-24