求函数Z=x^xy的偏导数

答案是Z=f✀x(x,y)=yx^xy(lnx+1),Z=f✀y(x,y)=x^(xy+1)lnx,求解答过程
2025-03-11 01:29:43
推荐回答(3个)
回答1:

Z=f'x(x,y)=xy*[x^(xy-1)]*y

Z=f'y(x,y)=xy*[x^(xy-1)]*x

回答2:

自变量在指数上的,简单的方法是取对数,相信见到过这种方法奥

回答3:

z = x^(x y)
lnz = xylnx
(1/z)f'x(z) = xy(1/x) + (lnx) (y)
= y+ylnx
f'x(z) = (1+lnx)z = y(1+lnx)(x^(xy))

lnz = xylnx
(1/z) f'y(z) = xlnx
f'y(z) = z(xlnx) =(z^(xy) ) xlnx