Use the Chain Rule to find the indicated partial derivatives. z = x^4 + xy^3, x = uv^4 + w^3, y = u + ve^w Find : ∂z/∂u , ∂z/∂v
, ∂z/∂w when u = 1, v = 1, w = 0
1 answer:
I'll use subscript notation for brevity, i.e. .
By the chain rule,
We have
and
When , we have
and the partial derivatives take on values of
So we end up with
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