10Q4 - ~v =-2 ~ j 2 ~ k at the point(1,1-1 4(5 pts(a...

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Name: Quiz 4 1. Find the partial derivatives: (a) (2 pts) P ( x, y ) = 3 x 5 - 2 xy + x 4 - y ; P x ( x, y ) = · · · (b) (2 pts) f ( x, y ) = y ln ± x 2 y ! ; f y ( x, y ) = · · · (c) (2 pts) g ( u, v ) = uv 2 2 u 2 + 3 v ; g u ( u, v ) = 2. (4 pts) Find an equation of the tangent plane to the graph of the function f ( x, y ) = cos x +3 y 2 at the point(0,1,4).

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3. (5 pts) Find the directional derivative of the function f ( x, y, z ) = 3 x 2 z + xyz 2 in the direction of the vector
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Unformatted text preview: ~v =-2 ~ j + 2 ~ k at the point (1,1,-1). 4. (5 pts) (a) Suppose the function f ( x, y ) has continuous partial derivatives. Use the chain rule to write a formula for the derivative of the function F ( t ) = f (5 t 3 , t 2 ) . (b) If f x (5 , 1) =-2 , f y (5 , 1) = 3 , ﬁnd the derivative F (1) ....
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10Q4 - ~v =-2 ~ j 2 ~ k at the point(1,1-1 4(5 pts(a...

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