Calculating Total Differentials of f(x,y) and P(R,T,V) | Function Examples

[Riles246]

total differentials!

a.) f = 1/(x+y²)

b.) f = ln(x²y)

c.) P = [(RT)/(V-B)]-[A/(T^1/2V²)]

what are the total differentials of these functions?

 

[cristo]

You need to show some work before we can help you. E.g. what is the definition of a total differential? What have you tried for each question?

 

[Riles246]

so far these are the answers I have come up with...

A. [-1/((x+y²)²)]dx - [2y/((x+y²)²)]dy
I started this problem by moving the denominator up but i am not sure that was the correct first move.

b. (2xy/x²y)dx + (x²/x²y)dy

c. I was not sure where to start with this problem.

 

[cristo]

so far these are the answers I have come up with...

A. [-1/((x+y²)²)]dx - [2y/((x+y²)²)]dy
I started this problem by moving the denominator up but i am not sure that was the correct first move.

b. (2xy/x²y)dx + (x²/x²y)dy

c. I was not sure where to start with this problem.

First two are correct. For the third, just do the same thing you've done in the first two, but this time the expression will have 5 terms.

 

[Riles246]

for part C I assumed that A,B, and R are constants and the answer I came up with is..

[-RT(V-B)^-2-AT^-1/2*-2V^-3)+(R/(V-B)+1/2AT^-1.5V^-2]

 

[Dick]

Shouldn't there be a dT and a dV in there, as there were dx and dy in the other cases?

 

[Riles246]

Woops. I forgot to put those in. Thanks!