Quandaries and Queries


differentiate Y=X^X^X


Hi Kunle,

First you have to decide if this is

y = x(xx)


y = (xx)x

Rather than making a choice I want to look at

y = xf(x)

To differentiate this expression first take the natural logarithm of both sides to get

ln(y) = ln( xf(x) ) = f(x) ln(x)

Differentiating both sides gives

 y'/y = f'(x) ln(x) + f(x) 1/x


y' = y ( f'(x) ln(x) + f(x) 1/x) = xf(x) ( f'(x) ln(x) + f(x) 1/x )

This should allow you to answer your queation.




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