Partial Derivatives: Solving T(x,t)=S(n) Chain Rule Mistake

[astoria]

T(x,t)=S(n) where n is some given function of x and t.


Why is (partial dT by partial dt)=dS/dn*(partial dn by partial dt)

What happens to the extra (all partials) (dS/dx)*(dx/dt)

I guess I'm misunderstanding the chain rule in partial derivatives but can someone point out my mistake.

Thanks

 

[vela]

S is a function of only n, so you don't differentiate it with respect to x. Where ∂x/∂t will show up is when you differentiate n with respect to t because n=n(x,t).