设函数z=sin(x^2y^2)+3x-5y^2+1,求dz
问题描述:
设函数z=sin(x^2y^2)+3x-5y^2+1,求dz
答
dz=[2xy^2cos(x^2y^2)+3]dx+[2x^2ycos(x^2y^2)-10y]dy
答
z=sin(x²y²)+3x-5y²+1所以δz/δx=cos(x²y²)*2xy²+3δz/δy=cos(x²y²)*2x²y-10y所以dz=(δz/δx)dx+(δz/δy)dy=[cos(x²y²)*2xy²+3]dx+[cos(x²y&...