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magicterry February 24th, 2018 03:57 AM

What is the differential of y =(A^x -B^x)^(1/x) ?

I make it dy/dx = (1/x)*(A^x - B^x)^(1/x-1)*(A^x -B^x)*LOGe(10)

= (1/x)*(A^x - B^x)^(1/x)*LOGe(10)

but trials show this is wrong, because y change for x change by 1 is less than
this increasingly less as x increases.

Where am I going wrong and what is the correct differential?:confused::confused::confused:

greg1313 February 24th, 2018 04:04 AM

See here. (W|A).


Take the natural logarithm of both sides:


Differentiate implicitly with respect to $x$:


I'll let you finish up. ;)

magicterry February 24th, 2018 04:24 AM

Thank you for such a quick reply:)

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