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melanie.dee:
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:
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:
thanks argh fuck i realised what i did.. im an idiot. thanks a lot!

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