Question

if x>0, what is the derivative of the function f(x) = x^x?​

Answer 1

Answer:

Step-by-step explanation:

y = x^x             .....(ln both sides)

ln y = x lnx       ......( differentiate )    

1/y . y' = lnx + x . 1/x

1/y . y' = ln x + 1

y' = y(ln x + 1)

y' = x^x(ln x + 1)

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