Theory and Examples

Find the point on the sphere 2 + ()2 + ()2 = 4 nearest

a. the xy-plane. b. the point (0, 7, -5).

MATH 2450 WEEK 6 Chain Rule in Higher Dimensions g(t) = df(x(t) , y(t))= ∂f * dx + ∂f * dy dt ∂x dt ∂y dt R(t) = < x(t), y(t), f( x(t), y(t) ) df(g(t)) = df * dg dt dg dt 2 EX. Use the chain rule to find the df/dt of the function f(x,y) = x + 3xy where x(t) = cos(t) and y(t) = sin(t) Fx= 2x + 3y Fx=...