Question

Find derivative of the following problem ?

Answer 1

Let u = x.lnx, , w= x and t = lnx;  w' =1 ;  t' = 1/x

f(x) = e^(x.lnx) ; f(u) = e^(u); f'(u) = u'.e^(u)

let' find the  derivative u' of u
u = w.t
u'=  w't + t'w;  u' = lnx + x/x = lnx+1

u' = x+1 and f'(u) = ln(x+1).e^(xlnx)

finally the derivative of f(x) =ln(x+1).e^(x.lnx) + 2x