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#### melanie.dee

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« on: November 07, 2007, 10:44:53 pm »
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i cant work out why my answer is wrong, and not what the solutions say. could someone please help me with this question

if y = xloge x/3 - x, find dy/dx

first problem is, i cant work out if the question means xloge(x/3) - x or xloge(x/3 - x)

i did it as though it was the former. and i think the solutions did too, except i cant really follow what they've done. anyway can someone explain the answer to that please

#### enwiabe

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« Reply #1 on: November 07, 2007, 11:06:41 pm »
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Using the product rule on xlog_e(x/3) and standard differentiation on '-x',

dy/dx = (derivative of 'x' multiplied by log_e(x/3)) + (derivative of log_e(x/3) multiplied by x) - (derivative of x)

= 1 x log_e(x/3) + x*(1/3)/(x/3) - 1
= log_e(x/3) + x/x - 1
= log_e(x/3) + 1 - 1
= log_e(x/3)

#### melanie.dee

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« Reply #2 on: November 07, 2007, 11:12:24 pm »
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thanks argh fuck i realised what i did.. im an idiot. thanks a lot!