z=x^(xy) 的偏導(dǎo)數(shù)?兩邊取對數(shù)：lnz = xy lnx∂lnz/∂x = ∂z/z∂x = y(lnx+1)∂z/∂x = z(lnx+1) = x^(xy) (lnx+1)y∂lnz/∂y = ∂z/z∂y = xlnx∂z/ͦ...

不是啦，你看錯題目勒是求z=x^x^y的偏導(dǎo)數(shù)，Y是x指數(shù)X的指數(shù)（有點(diǎn)繞口呵呵，我想你應(yīng)該能理解）

z=x^(x^y)lnz=(x^y) lnx∂lnz/∂x=yx^(y-1) lnx + x^y/x = yx^(y-1) lnx + x^(y-1) = x^(y-1)(ylnx+1)∂lnz/∂x = (1/z)∂z/∂x = x^(y-1)(ylnx+1)∂z/∂x = x^(y-1)(ylnx+1)x^(x^y) (1)∂lnz/∂y = (1/z)∂z/∂y = lnx(x^y)lnx∂z/∂y = lnx(x^y)lnx x^(x^y) = ln²x [x^(x^y+y)] (2)