C微积分运第曰 求偏导数运算 1.求多元函数的导数 2.求隐函数的导数 (1)设f(xy):=x2·sin(x+y),求偏导数 fxy)的图形 f(x,y)>2.x sin(x+y)+xcos(x+ y f(x,y)→2sin(x+y)+4xcos(x+y)-x·sin(x+y) y) f(x,y)→2.xcos(x+y)-x·sin(x+y) 0 f(x,y,z): =sin(x)++ sin(y) f(x,y,z)→ sin(x) cos(x) (sin(x)+ sin(y)+ sin(z) gx, y)--gx, y) simplify> exp(x)+ exp(y)) (exp(x)+ exp(y))
x g(x,y) ¶ ¶ y g(x,y) ¶ ¶ - simplify -(-exp(x) + exp(y)) (exp(x) + exp(y)) g(x, y) ln e ® x e y := ( + ) x f(x,y, z) ¶ ¶ 1 sin(x) 2 sin(y) 2 + sin(z) 2 ( + ) 1 2 ® ×sin(x)×cos(x) f(x, y, z) sin(x) 2 sin(y) 2 + sin(z) 2 := + v f(u,v) ¶ ¶ 1 9 p 2 × cos 1 2 ×p æ ç è ö ÷ ø ® × = 0 u f(u,v) ¶ ¶ 2 3 ×p sin 1 2 ×p æ ç è ö ÷ ø × 1 9 p 2 × cos 1 2 ×p æ ç è ö ÷ ø v ® + × = 2.094 p 6 u := p 3 := x y f(x, y) ¶ ¶ ¶ ¶ 2×x×cos(x + y) x 2 ® - ×sin(x + y) 2 y f(x,y) ¶ ¶ 2 x 2 ® - ×sin(x + y) 2 x f(x,y) ¶ ¶ 2 2×sin(x + y) 4×x×cos(x + y) x 2 ® + - ×sin(x + y) y f(x,y) ¶ ¶ x 2 ® ×cos(x + y) x f(x,y) ¶ ¶ 2×x×sin(x + y) x 2 ® + ×cos(x + y) f(x,y)的图形 f (1) 设 f(x, y) x 2 := ×sin(x + y) , 求偏导数. 1. 求多元函数的导数. 2. 求隐函数的导数. 实验3 微积分运算(三) 求偏导数运算
(2)已知方程山2+y2)=an2)确定的隐函数求 F(x,y) simplify→(x+y) F(x, y) simplify -(-y+x) (x2 F(x,y) (x+y) F(x,y)
(2) 已知方程 ln x 2 y 2 + ( ) atan y x æ ç è ö ÷ ø = 确定的隐函数, 求 dy dx . F(x, y) ln x 2 y 2 + ( ) atan y x æ ç è ö ÷ ø := - dy dx F x - F y = x F(x, y) ¶ ¶ simplify (x + y) x 2 y 2 ( + ) ® y F(x, y) ¶ ¶ simplify -(-y + x) x 2 y 2 ( + ) ® D(x,y) x F(x, y) ¶ ¶ y F(x, y) ¶ ¶ := - D(x,y) simplify (x + y) (-y + x) ®
