Question

一道高数题 ，不知道怎么求导，第二题

Answer 1

let
z=y^x
lnz = xlny
(1/z) dz/dx = (x/y) y' + lny
dz/dx = [(x/y) y' + lny] .y^x

let
p= x^y
lnp = ylnx
(1/p) dp/dx = y/x + (lnx)y'
dp/dx =[y/x + (lnx)y' ] .x^y

y^x = x^2 +x^y
[(x/y)y' + lnx].y^x = 2x +[ ( y/x + lnx. y' )] x^y
[ x.y^(x-1) -2lnx .x^(y+1) ] y' = 2y - lnx.y^x
y' = (2y - lnx.y^x) /[ x.y^(x-1) -2lnx .x^(y+1) ]