Unformatted text preview: at the point (1,l). (b) (8 points) Find the directional derivative of (r+y)F(x,y) at the point (1,1) in the direction of the vector 4.4>-4, (25 points) Suppose F is a differentiable function of three variables, and we define a function G of two variables by G(x,y) = F(x*y, xy, x). (a) (13 points) Express the partial derivatives of G(a y) with respect to .r and y in terms of F and its partial derivatives FI, F2, F3. (b) (12 points) T-et (a,b) be a point of the plane, and C the level curve to the function G(x,y) (defined above) which passes through (a,b). Find the equation of the tangent line to C at (a,b) in terrrs of the value andpartial derivatives of .F. 5. (15 points) Suppose u and u are differentiable functions of two variables. Derive the formula Y (u/u) - (uY u - uY u)/uz....
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- Spring '08
- Parametric equation, 30m, 5 3m, MOFFITT L IBRARY, George M. Bcrgman