几道大一的高数题2,给出计算过程.
几道大一的高数题2,给出计算过程.
几道大一的高数题2,给出计算过程.
几道大一的高数题2,给出计算过程.
抢个沙发算了，过程挺复杂的，至少我这样认为，因为我不大会用word文档的公式编辑器。
5
z=f(x^2-y^2,e^xy)
(x^2-y^2)'x=2x (e^xy)'x=ye^xy (x^2-y^2)'y=-2y (e^xy)'y=xe^xy
dz/dx=z'x=f'(x^2-y^2)*(x^2-y^2)'x+f'(e^xy)*(e^xy)'x=f'(x^2-y^2)*2x+f'(e^xy)*(ye^xy)
dz/dy=z'y=f'(x^2...
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5
z=f(x^2-y^2,e^xy)
(x^2-y^2)'x=2x (e^xy)'x=ye^xy (x^2-y^2)'y=-2y (e^xy)'y=xe^xy
dz/dx=z'x=f'(x^2-y^2)*(x^2-y^2)'x+f'(e^xy)*(e^xy)'x=f'(x^2-y^2)*2x+f'(e^xy)*(ye^xy)
dz/dy=z'y=f'(x^2-y^2)*(x^2-y^2)'y+f'(e^xy)*(e^xy)'y=f'(x^2-y^2)*(-2y)+f'(e^xy)*(xe^xy)
6
y=x^2-54/x (x<0)
y'=2x+54/x^2 y'=0 2x=-54/x^2,x=-3, x<-3,y'<0,随着x减小,y增大,x>-3,y'>0随着x增加,y增加,
x=-3时,y最小值=9+18=27
7
f(x,y)=x^3-y^3+3x^2+3y^2-9x
f'x=3x^2+6x-9 f'x=0 x=1或x=-3
f'y=-3y^2+6y f'y=0,y=0或y=2
极值f(1,0)=-6,f(1,2)=-2, f(-3,0)=27,f(-3,2)=31
收起