find the derivative of ;d/dx(In2x)

Question

help me show all the working

Answer 1

Question: find the derivative of ;d/dx(In2x).

Let y = ln(2x), then

dy/dx = d/dx(ln(2x))

Now y = ln(2x) = ln(2*x) = ln(2) + ln(x)

Since ln(2) is just a constant, then its derivative is zero.

i.e. dy/dx = 0 + 1/x

dy/dx = 1/x

So, d/dx(ln(2x)) = 1/x

Answer 2

ln2x=

if the derivative of lnx =1/2*d(x)/dx but the derivative of x is 1 so it will be 1/2*1=1/2

therefore the derivative of ln2x will be ln2x=1/2x*d(2x)/dx but the derivative of 2x is 1

so it will be 1/2x*2=2/2x

 2/2x=1/x

dy/dx=1/x