z=x^y+y^x求dz/dx

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z=x^y+y^x求dz/dx
z=x^y+y^x求dz/dx

z=x^y+y^x求dz/dx
两边同时取对数,有
ln z = ylnx+xlny
上式两边对X求导,有
1/z dz/dx=y/x + lny
所以
dz/dx=(y/x + lny)(x^y+y^x)

z=x^y+y^x
dz/dx = y*x^(y-1) + (y^x) *lny

z=x^y+y^x
dz/dx = y*x^(y-1) + (y^x) *lny
dz/dx
=y*x^(y-1)+lny*y^x

先把d约去

dz/dx
=y*x^(y-1)+lny*y^x