#" "#
#y# is composite of two functions #" lnx" " and (1 - 2x)^3 #
#" "#
Let #u(x)= lnx " and " v(x) = (1-2x)^3" #
#" "#
Then, #" y=u(v(x))" #
#" "#
Differentiating this function is determined by applying chain rule.
#" "#
#color(red)(y' = u'(v(x))xxu'(x))#
#" "#
#color(red)(u'(v(x)) = ?)#
#" "#
#u'(x) = 1/x#
#" "#
#u'(v(x))) = 1/(v(x))#
#" "#
#" "#
#color(red)(u'(v(x)) = 1/(1-2x)^3)#
#" "#
#" "#
#" "#
#color(red)(v'(x) = ?)#
#" "#
#v'(x) = 3(1-2x)^2(1-2x)'#
#" "#
#v'(x) = 3(1-2x)^2(-2)#
#" "#
#color(red)(v'(x) = -6(1-2x)^2)#
#" "#
#" "#
#color(red)(y' = u'(v(x))xxu'(x))#
#" "#
#y' = 1/(1-2x)^3 xx -6(1-2x)^2 #
#" "#
#y' = (-6(1-2x)^2)/(1-2x)^3 #
#" "#
#y' = -6/(1-2x) #
