Find dy/dx of y= the square root of ln x

  • #1

Homework Statement


Find dy/dx when y=[itex]\sqrt{ln x}[/itex]


Homework Equations


d/dx of ln x is equal to 1/x times d/dx of x.


The Attempt at a Solution


I tried to raise the ln x to the 1/2 power instead of keeping it under a square root sign, but I had no luck. I'm struggling with Calculus. I would very much appreciate some help.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
DryRun
Gold Member
838
4
To visualize the problem in an easier way, let u = ln x. Then proceed. First, differentiate the power, then the term/s under the square root.
 
  • #3
52
0
I tried to raise the ln x to the 1/2 power instead of keeping it under a square root sign, but I had no luck.

This strategy for solving the problem won't work because (ln(x))^a ≠ln(x^a) = a*ln(x). As suggested by sharks, u substitution is the best strategy here.
 
  • #4
67
0
Using u-sub:


[itex]\frac{dy}{dx}[/itex][itex]\sqrt{lnx}[/itex] | u=lnx

=[itex]\sqrt{u}[/itex]'*u'

=[itex]\frac{1}{2\sqrt{lnx}}[/itex]*[itex]\frac{1}{x}[/itex]

=[itex]\frac{1}{2x\sqrt{lnx}}[/itex]

It's been a while since I've done derivatives, but I think this should be the correct way of working it.
 
  • #5
dextercioby
Science Advisor
Homework Helper
Insights Author
13,050
598
There's a nice trick at hand.

[tex] y^2 (x) = \ln x [/tex]

Differentiate both sides with respect to x.
 

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