Derivative of c= (2p/q)-1/2: Step-by-Step Solution and Tips

[babypudding]

Homework Statement

Find dc/dp and dc/dq.

Homework Equations

c= (2p/q)^-1/2

The Attempt at a Solution

I just want to make if I'm right. I got...
dc/dp = (2/q)^-1/2

dc/dq = [-2p/(q^2)] ^-1/2

Thanks.

 

[happyg1]

Hi,
There is an error in your use of the chain rule:
$$\frac{dc}{dp}=-\frac{1}{2}\left(\frac{2p}{q}\right)^{-\frac{3}{2}}\cdot\left(\frac{2q-0}{q^2}\right)$$
then simplify.

Same thing for dc/dq:
$$\frac{dc}{dq}=-\frac{1}{2}\left(\frac{2p}{q}\right)^{-\frac{3}{2}}\cdot\left(\frac{0-2p}{q^2}\right)$$
then simplify.