Thread: Help, I'm stuck in these 3 differentials problems

What we saw in class was too basic... examples of these are not even in the book we are using.


Help is appreciated, thank you!



4)Find the total differential dz = zxdx + zydy for the following function:
z = 7x2ye




16)Find the total differential dz = zxdx + zydy for the following function:
z = (9y3) / (x-y)


This last one has economics application.

19)Consider the following system of equations:
Y = C + I0 + G0
Yd = Y - T (disposable income)
C = C0 + bYd
T = T0 + tY
A. Solve for the equilibrium level of output.
B. What is the government spending multiplier, dY/dG?
C. What is the balanced-budget multiplier (that is, what is dY when dG and dT exactly offset each other)?
D. Is this positive or negative? Greater than or less than 1?

First, please write the problems unambiguously. If the "2" in "7x2" is supposed to be an exponent, write it as "7x^2". And if the "x" in "dz= zxdx+..." is a subscript, write it as "dz= z_x dx+...".

Now, what have you done yourself? If z= 7x^2y^e (and is that really an exponent of "e", not, perhaps, 3?), then what are z_x and z_y?