# Math Help - help needed for partial D qn

1. ## help needed for partial D qn

Hi All,
I got a problem tat i cant solve. pls help!

w is a function
w= -x to the power of 1/2 x F(z)

and z= y/2 x 1/( x to the pwer of 1/2)

the qns are as follow:

if u = -(dz/dy)
derive an expression for u in terms of F' where F' is dF/dz

Jae

2. Please don't use "x" both for a variable and as a multiplication sign! Use "*" or, better, use LaTex.

I think you mean that
$w= -x^{1/2}F(z)$
which also says that $x^{1/2}= -\frac{w}{F(z)}$

$z= \frac{y}{2}\frac{1}{x^{1/2}}$

Those two together tell us that
$z= -\frac{y}{2}\frac{F(z)}{w}$

It isn't clear whether w is independent of y or not. Assuming it is, we can differentiate both sides with respect to y to get
$\frac{dz}{dy}= -\frac{1}{2}\frac{F(z)}{w}- \frac{y}{2}\frac{F'(z)}{w}\frac{dz}{dy}$

Solve that algebraically for u.