# Differentiation of two similar systems

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1. Nov 13, 2014

1. The problem statement, all variables and given/known data
Hi. i need help with understanding task with differentiation.
i have two separate tasks, and i need help understanding why the solutions differ somewhat.
system 1:
Y = C + I + G
C = f(Y-T)
I = h(r)
r = m(M)

system 2:
Y = C + I + G
C = F(Y,T,r)
I = f(Y,r)

in system 1. when differentiating system 1, the "C-equation", the book gives then answer f'(dY - dT),,,, the derivative is not specified to be in respect to Y or T.
in system 2, when differentiating the C-equation", the book gives the answer: f'(Y)*dY + f'(T)*dT + f'(r)*dr
the symbol in the parentheses are meant to tell in what respect the derivation is.
the question is, why are the differentiating ( only of the C-equation, i know how the rest) different?

Mons
2. Relevant equations

3. The attempt at a solution

2. Nov 13, 2014