
Junior Member
Concepts of relationships of fcns & their deriv's: w = f(x,y,z)= f(r(t)) = g(t)
Hello All,
Given:
f : R^{3}→R
r : R→ R^{3}represents position of moving object as a function of time
g(t) is valueof f at the object’s position at time t
Firstquestion:
Is all thiscorrect for me to say:
w = f(x,y,z)= f(r(t)) = g(t)
Secondquestion:
Are partialderivatives of w and of f the same, in other words, do:
∂w/∂x = ∂f/∂xand ∂w/∂y = ∂f/∂y and ∂w/∂z = ∂f/∂z
Thirdquestion:
Arederivatives with respect to t all equal, in other words, do:
df/dt = dg/dt= dw/dt
Trying tounderstand correct concepts and relationships between all the elements of thisexercise, so I hope my questions make sense.
Thank you

Junior Member
Hello All,
Can ignore this.
I was able to confirm answers to all 3 questions are all "yes".
Thank you
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