数学分析(复旦大学版)课后题答案14章.pdfVIP

210 1›oÙ  êÚ‡© §1.  êÚ‡©Vg 1. ¦e¼ê êµ (1) z = x2 ln(x2 + y2 ) (2) u = exy x (3) z = xy + y y (4) u = arctan x (5) u = x2 + y2 + z2 + 2xy + 2yz + 2zx (6) u = eϕ−θ cos(θ + ϕ) ) µ 2 2 2 2 x 2x y (1) zx = 2x ln(x + y ) + 2 2 , zy = 2 2 . x + y x + y (2) ux = yexy , uy = xexy . 1 x(y2 − 1) (3) zx = y + , zy = 2 . y y y x (4) ux = − 2 2 , uy = 2 2 . x + y x + y (5) ux = 2(x + y + z), uy = 2(x + y + z), uz = 2(x + y + z). (6) uϕ = eϕ−θ [cos(θ + ϕ) − sin(θ + ϕ)], uθ = −eϕ−θ [sin(θ + ϕ) + cos(θ + ϕ)]. 2 2 2. f (x, y) = x y − 2y §¦f (x, y), f (x, y), f (2, 3), f (0, 0), f (x, y) x=y . x y x y y y=x 2 2 2 ) µf (x, y) = 2xy , f (x, y) = 2x y − 2, f (2, 3) = 36, f (0, 0) = −2, f (x, y) x=y = 2xy − 2 x y x y y y=x ∂z ∂z 1 3. z = ln(√x + √y)§y ²x + y