2. Partial Differentiation - MIT OpenCourseWare
−(y −x). (x + y)2 (x + y)3 (x + y)2 (x + y)3 c) fx = −2xsin(x2 + y), fxy = (fx)y = −2xcos(x2 + y); fy = −sin(x2 + y), fyx = −cos(x2 + y)· 2x. d) both sides are f0 (x)g 0 (y). 2A-4 (fx)y = ax+6y, (fy)x = 2x+6y; therefore fxy = fyx a = 2. By inspection, 2 2 ⇔ one sees that if a = 2, f(x,y) = x y +3xy is a function with the given fx ... ................
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