SOLUTION: Find the derivative of y with respect to x. y=ln(ln 2x)

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Question 1189627: Find the derivative of y with respect to x.
y=ln(ln 2x)
Found 3 solutions by MathLover1, ikleyn, Alan3354:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
y=ln%28ln+%282x%29%29
Find the derivative of y with respect to x.

%28d%2Fdx%29%28ln%28ln%282x%29%29%29..........apply chain rule

=%281%2Fln%282x%29%29%28d%2Fdx%29%28ln%282x%29%29

so, %28d%2Fdx%29%28ln+%282x%29%29=1%2Fx, and we have

=%281%2Fln%282x%29%29%281%2Fx%29............simplify

=1%2F%28x%2Aln%282x%29%29

answer: y'%28x%29+=+1%2F%28x%2Alog%282+x%29%29



Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.

The answer is   y' = 1%2F%28x%2Aln%282x%29%29,


and the domain of the function is   x > 1/2   to provide   ln(2x) > 0.




Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the derivative of y with respect to x.
y=ln(ln(2x))
-----------------------------
y' = 2%2Fln%282x%29%2F%282x%29+=+1%2F%28x%2Aln%282x%29%29