The discussion revolves around finding the derivative of a function F with respect to the variable M, where F is defined in terms of M and T, with T being a variable and Tc, a, and b as constants. The participants are exploring the implications of treating T as a variable versus a constant in the context of differentiation.
There is an ongoing exploration of the relationship between T and M, with some participants suggesting that if T is indeed a variable dependent on M, then the chain rule applies. However, there is a lack of consensus on how to proceed without additional information regarding the relationship between T and M.
Participants note that a, Tc, and b are constants, while the status of T is debated, impacting the differentiation approach. The original problem statement requires finding the total derivative dF/dM, which adds complexity to the discussion.
steejk said:Homework Statement
F = 1/2.a(T-Tc)M^2 + 1/4.bM^4
I need to find dF/dM
a,Tc,b are positive constants
2. The attempt at a solution
I assume this is to do with partial derivatives etc.
So I found:
∂F/∂T = 1/2.aM^2
∂F/∂M = TaM - TcaM + bM^3
And using a chain rule:
dF/dM = ∂F/∂T.dT/dM + ∂F/∂M.dM/dM
But not sure how to find dT/dM
LCKurtz said:Is that supposed to be$$
F=(\frac 1 2)a(T-T_c)M^2 +(\frac 1 4)bM^4$$
steejk said:Homework Statement
F = 1/2.a(T-Tc)M^2 + 1/4.bM^4
I need to find dF/dM
a,Tc,b are positive constants
steejk said:Yes that's the correct equation.
Isn't T also a variable or have I just forgotten how to do basic differentiation?
LCKurtz said:You said it was a constant above. And if it weren't, you would still calculate the partial derivative ##\frac{\partial F}{\partial M}## the same way.