Partial derivative chain rule question

[engineer_dave]

Homework Statement

Given z= square root of xy, x = 2t - 1, y = 3t +4, use the chain rule to find dz/dt as a function of t.

Homework Equations

The Attempt at a Solution

dz/dt = partial derivative of z with respect to x multiplied by dx/dt + (partial derivative of z with respect to y multiplied by dy/dt)

I got that part right but how do you differentiate square root of xy as a partial derivative of z with respect to x?? Can you show me the final answer of that?

Thanks!

 

[bob1182006]

take y as a constant and find the partial derivative of z=sqrt(xy) like you normally would.

 

[engineer_dave]

yea i tried that but could u give me the final answer to that particular part. would it 1/2x^-1/2 multiplied by y?

 

[bob1182006]

you're missing a y with the x, it should be $$\frac{(xy)'}{2\sqrt{xy}}$$

where (xy)'=y

when you take the partial derivative you're just leaving y as constant so the y stays with x under the square root.