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Answer 1 · 2016-08-18T17:27:16

#(dy)/(dx) =-1/(xln(x))#

We have #y(u(x))# so need to use the chain rule:

#u(x) = -1/ln(x)#

# implies (du)/(dx) = 1/(xln^2(x))#

#y = ln(u) implies (dy)/(du) = 1/u = -ln(x)#

#(dy)/(dx) = (dy)/(du)(du)/(dx)#

#(dy)/(dx) = -ln(x)*1/(xln^2(x)) = -1/(xln(x))#