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find slope at (7,0) using logarithmic differentiation

Mathematics
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i did like this : |dw:1346421919918:dw|
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Other answers:

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@AravindG follow this : http://scidiv.bellevuecollege.edu/dh/Calculus_all/CC_2_9_ImplicitDiff
now when i put x=7 i am stuck!
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ya i cant find slope at (7,0)
the answer is 1/20
@Mimi_x3 , @UnkleRhaukus please help
Well Ar. I read up on this nice tool Logarithm differentiation. Thx for the news But I can show that it is quite works well here
how?
1 Attachment
in btw hapy that i could tell u sthng new :) its very hand for big eqns
Now WRITE THE SPECIAL CASE of YOURS CAREFULLY with this:
\[(x-7)/(x-2)(x-3)*[ \frac{ 1 }{ x-7 } - \frac{(2x -5)}{(x-2)(x-3)}]\]
Now the FIRST fraction IS REDUCED and the second evaluates to zero at x=7
\[=\frac{ 1 }{ (x-2)(x-3)}\]
= 1/20
See again my attachment
the more prosaic way to look at this is when you multiply by the original function the \(x-7\) cancels
that's what i said above
yes, it is nice
Guru -can you put some explanations whether one has a chance to become YOUR moderatot ?
gt it !!!! thx a lot @satellite73 and @Mikael

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