What is the derivative of the square root of 2x using the chain rule?

[chebyshevF]

Homework Statement

Find the derivative of:
f(x)=\sqrt{2x}

Homework Equations

So using the chain rule: \frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx}

The Attempt at a Solution

Isn't it just a simple matter of setting u=2x, therefore du/dx=2, and y=\sqrt{u}=u^1/2, therefore dy/du=1/2 * u^(-1/2)
Therefore dy/dx = 1/2 *2x^(1/2) . 2
finally = 2x^(-1/2)

Is this correct? The solutions say that the answer is 1/2 * sqrt(2x)^-1/2

 

[ppzmis]

So long as your answer is (2x)^(-1/2) not 2*x^(-1/2) then you are correct and the solution is wrong.

 

[chebyshevF]

Thanks.
But isn't 2x the same as saying 2*x ?

 

[ppzmis]

Thanks.
But isn't 2x the same as saying 2*x ?

I just wanted to be clear that the square root applied to the 2 and the x and not just the x hence the brackets

 

[HallsofIvy]

Thanks.
But isn't 2x the same as saying 2*x ?

Yes, but (2x)^{1/2} is NOT the same as 2x^{1/2}!