@Adri van der Meer 

This does give the correct answer and it does work but, for instance when it returns the answer to 

e3 := vx = diff(Phi(x,y),x);

I would like f(y*sqrt(U*v/x)) be returned as f(eta) and D(f)(y*sqrt(U*v/x)) to just  be f'(eta) 

I think I need to use the declare comand but, I am not sure how to use it in this case. 

Thank you for your help. 

e1:=η(x,y)=y*sqrt(U*v/x)

e2: = Φ(x,y)=sqrt(U*v*x)*f(η)

e3:=v_y=∂Φ(x,y)/∂x

e4:=vx=∂Φ(x,y)/∂y

I would like e3 and e4 to return something along the lines of (e3 for example) 

∂Φ(x,y)/∂y=sqrt(U*v*x)*∂f(η)/∂η*∂η/∂y=sqrt(U*v*x)*f'(η)*sqrt(U/v*x)=U*f'(η)

Hopefully everyone can see these equations. I have tried to attached the worksheet once again with the equtations just to see if it might decide to work. 

-KM

@kminor2578 @Carl Love

Cancel that last post seems that it didnt work. Are there any other options?

@Carl Love 

Seems to work now. Thanks again

MaplePrimes_Uploa.mw

@Carl Love 

attached is a work sheet with the equations. Thanks for the heads up.

MaplePrimes_Uploa.mw