What is the derivative of #f(x)=(x1)^2/ln(1/x)^2#?
1 Answer
For the big picture, it's quotient rule. For both numerator and denominator, we'll need separate chain rules.
Explanation:

Quotient rule: be
#y=f(x)/g(x)# , then#y'=(f'gfg')/g^2# 
Chain rule:
#(dy)/(dx)=(dy)/(du)(du)/(dx)#
Let's find the derivatives of both numerator and denominator separately then aggregate them up afterwards.

Numerator: let's rename
#u=x1#
#(deltay)/(deltax)=2u(1)=2x2# 
Denominator: let's rename
#u=1/x# and#v=ln(u)#
#(deltay)/(deltax)=(2v)/(ux)=(2ln(1/x))/((1/x)(x^2))=(2ln(1/x))/x#
Now, let's derivate the whole quotient: