Where am I messing up?

Use logarithmic differentiation to find the derivative of the function. y= sqrt(x)^7/x
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I will post my work below.

Question

Where am I messing up?

Use logarithmic differentiation to find the derivative of the function. y= sqrt(x)^7/x
-------------------

I will post my work below.

turingtest · Answer

$$ y= \sqrt{x^7}/x=x^{7/2}/x=x^{5/2}$$if your formula is written correctly you can first simplify it this way. Is this written correctly?

anonymous · Answer

$$lny=lnx^{7x/2}$$

$$u=7x/2$$

$$lny=ulnx$$

$$(1/y) (dy/dx) = (7x/2)(1/x)+(lnx)(7/2)$$

$$(dy/dx) = [(7x/2)(1/x)+(lnx)(7/2)]    [(\sqrt{x})^{7x}]$$

turingtest · Answer

so x is in the exponent too?

anonymous · Answer

Oops, the question is actually, i wrote it wrong. 

$$(\sqrt{x})^{7x}$$

anonymous · Answer

I'm being told that my final answer is wrong. Yet i can't figure out where I am messing up.

turingtest · Answer

$$y=\sqrt{x}^{7x}$$ right? let me try it for a minute...

anonymous · Answer

Yes Turing, that's right.

By the way, I really appreciate you taking the time to help me.

turingtest · Answer

I got the same as you but noticed that in the last line the (7x/2)(1/x) cancels to 7/2
so
$$y'=(7/2)(1+\ln x)\sqrt{x}^{7x}$$I hope that works...

anonymous · Answer

Boom, that was the problem.

Thanks, you're awesome!

turingtest · Answer

Sweet, but you did it pretty much yourself. I just saw a detail, that's why two heads are better than one :)