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

[Interception]

Homework Statement

Find dy/dx when y=$\sqrt{ln x}$

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.

 

[DryRun]

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.

 

[jmcelve]

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.

 

[danielu13]

Using u-sub:


$\frac{dy}{dx}$$\sqrt{lnx}$ | u=lnx

=$\sqrt{u}$'*u'

=$\frac{1}{2\sqrt{lnx}}$*$\frac{1}{x}$

=$\frac{1}{2x\sqrt{lnx}}$

It's been a while since I've done derivatives, but I think this should be the correct way of working it.

 

[dextercioby]

There's a nice trick at hand.

$$y^2 (x) = \ln x$$

Differentiate both sides with respect to x.