求z对x的导数时,把y当成常数看待;求z对y的导数时,把x当成常数看待即可。
lnz=x^2*ln(x+2y)①两边对x求偏导1/z*dz/dx=2x*ln(x+2y)+x^2/(x+2y)dz/dx=[2ln(x+2y)+x/(x+2y)]*x(x+2y)^(x^2)②两边对y求偏导1/z*dz/dy=2x^2/(x+2y)dz/dy=2x^2/(x+2y)*(x+2y)^(x^2)=2x^2*(x+2y)^(x^2-1)