logarithmic differentiation

[sully405]

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.

 

[askmemath]

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

 

[elchichita]

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