Calculuspartial derivatives
posted by mark on .
Let Z = f(u,v) where u=xy^3 + e^3 and v = (x^2)y.
Obtain expressions for Zx and Zy in terms of fu and fv.
I don't understand the "in terms of" part. How do I do this question? thank you

dZ = Zx dx + Zy dy (1)
Also:
dZ = df = fu du + fv dv (2)
Express du and dv in terms of dx and dy:
du = ux dx + uy dy (3)
dv = vx dx + vy dy (4)
Substitute (3) and (4) in (2):
dZ = fu (ux dx + uy dy ) + fv (vx dx + vy dy) =
(fu ux + fv vx) dx + (fu uy + fv vy)dy
Comparing this to (1) then gives:
Zx = fu ux + fv vx
Zy = fu uy + fv vy