(11) Suppose that we substitute polar coordinates x = r cos 0 and y = r...

 

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(11) Suppose that we substitute polar coordinates x = r cos 0 and y = r sin in a differentiable function w = f(x, y). (a) Show that r 1 Ow r 20 = fx cos 0 + fy sin == - fr sin +fy cos 0. (b) Solve the equations above for fx and fy in terms of Ow/ar and 0. (c) Show that 2 1 + 72 () 2 (fx) + (fy)= = (3) (11) Suppose that we substitute polar coordinates x = r cos 0 and y = r sin in a differentiable function w = f(x, y). (a) Show that r 1 Ow r 20 = fx cos 0 + fy sin == - fr sin +fy cos 0. (b) Solve the equations above for fx and fy in terms of Ow/ar and 0. (c) Show that 2 1 + 72 () 2 (fx) + (fy)= = (3)