Posted by Vincent on .
Thermodynamics texts use the relationship (dy/dx)(dz/dy)(dx/dz) = 1
Explain the meaning of this equation and prove that it is true (Hint: Start with a relationship F(x,y,z) = 0 that defines x = f(y,z), y = g(x,z), and z = h(x,y) and differentiate implicitly)

Vector Calculus 
Steve,
This topic is discussed here:
http://books.google.com/books?id=6I7e_RQ5zD0C&pg=SA4PA30&lpg=SA4PA30&dq=thermodynamics+dz/dx+dx/dy&source=bl&ots=6MEOyqi1LQ&sig=54pfdB1Beh0A8_oxHCSP2anCk&hl=en&sa=X&ei=XolOUurLHIya8wTusIHYDQ&ved=0CDIQ6AEwAQ#v=onepage&q=thermodynamics%20dz%2Fdx%20dx%2Fdy&f=false