logarithmic differentiation

sully405

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May 19, 2005
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I have lots of formulas and examples on how to do logarithmic differentiation, but I do not know why, how are what you are supposed to do with it all.

y=(x-2)^(x+1)

Thanks for any help.
 
log y = (x+1)log(x-2)

(1/y)dy=(x+1)/(x-2)+log(x-2)

dy=y[(x+1)/(x-2)+log(x-2)]

but y=(x-2)^(x+1)

Substitute that back into the equation
 
Logarithmic differentiation is a technique to compute indirectly a derivative....Instead of differentiating the function, we differentiate the log of the function.....This technique simplifies the calculation, especially if the function has powers, like in the example you provided
 
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