# What is the derivative of #Ln(x)/(1+ln(2x))#?

##### 1 Answer

#### Explanation:

If you are studying maths, then you should learn the Quotient Rule for Differentiation, and practice how to use it:

# d/dx(u/v) = (v(du)/dx-u(dv)/dx)/v^2 # , or less formally,# (u/v)' = (v(du)-u(dv))/v^2 #

I was taught to remember the rule in word; " *vdu minus udv all over v squared* ". To help with the ordering I was taught to remember the acronym, VDU as in Visual Display Unit.

So with

# :. d/dx(u/v) = (v(du)/dx-u(dv)/dx)/v^2 #

# :. dy/dx = ( (1+ln(2x))(1/x) - (lnx)(1/x) ) / (1+ln(2x))^2#

# :. dy/dx = (1/x)(1+ln(2x) - lnx) / (1+ln(2x))^2#

# :. dy/dx = (1+ln(2x) - lnx) / (x(1+ln(2x))^2) #