Question

求偏导数： 1、f(x,y)=x+y+(x^2+y^2)^(1/2),求fx(3,4),fy(3,4) 2.f(x,y)=x+(y-1)arcsin(x/y)^1/2,

求fx(x,1)

Answer 1

1.fx(x,y)=1+(x^2+y^2)^(-1/2)*x,fy(x,y)=1+(x^2+y^2)^(-1/2)*y
所以代入得到结果是fx(3,4)=8/5,fy(3,4)=9/5
2.由于x是所求函数的导变量，所以将y=1代入原式再求导，得到结果为1

Answer 2

1
f(x,y)=x+y+(x^2+y^2)^(1/2)
f'x=1+x/(x^2+y^2)^(1/2) fx(3,4)=1+3/5=8/5
f'y=1+y/(x^2+y^2)^(1/2) fy(3,4)=1+4/5=9/5
2
f(x,y)=x+(y-1)arcsin(x/y)^(1/2)
f'x=1+(y-1)*(1/y)*(1/2)(y/x)^(1/2)*[1/[1-(x/y)]^(1/2)]
=1+[(y-1)/2]*[1/(x-x^2/y)^(1/2)]=1+[(y-1)/2]*[y/(x-x^2)]^(1/2)
fx(x,1)=1

Answer 3

1.fx(x,y)=1+y+x/[(x^2+y^2)^(1/2)] fx(3,4)=28/5
fy(x,y)=x+1+y/[(x^2+y^2)^(1/2)] fy(3,4)=24/5
2.对x求导，再把值代入即可

Answer 4

这里面x与y相互独立，对x求偏导的时候就把y的值先带进去，然后当成一元函数求导就行了，y也一样~