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Korolek [52]
3 years ago
11

Let w = x2 + y2 + z2, x = uv, y = u cos(v), z = u sin(v). use the chain rule to find ∂w ∂u when (u, v) = (9, 0).

Mathematics
1 answer:
jasenka [17]3 years ago
7 0
By the chain rule,

\dfrac{\partial w}{\partial u}=\dfrac{\partial w}{\partial x}\cdot\dfrac{\partial x}{\partial u}+\dfrac{\partial w}{\partial y}\cdot\dfrac{\partial y}{\partial u}+\dfrac{\partial w}{\partial z}\cdot\dfrac{\partial z}{\partial u}
\dfrac{\partial w}{\partial u}=2xv+2y\cos v+2z\sin v

We also have x(9,0)=0, y(9,0)=9, and z(9,0)=0, so at this point we get

\dfrac{\partial w}{\partial u}(9,0)=2\cdot9\cdot\cos0=18
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