设函数z=sin(x^2y^2)+3x-5y^2+1,求dz

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设函数z=sin(x^2y^2)+3x-5y^2+1,求dz

设函数z=sin(x^2y^2)+3x-5y^2+1,求dz
设函数z=sin(x^2y^2)+3x-5y^2+1,求dz

设函数z=sin(x^2y^2)+3x-5y^2+1,求dz
z=sin(x²y²)+3x-5y²+1
所以δz/δx=cos(x²y²)*2xy²+3
δz/δy=cos(x²y²)*2x²y-10y
所以dz=(δz/δx)dx+(δz/δy)dy
=[cos(x²y²)*2xy²+3]dx+[cos(x²y²)*2x²y-10y]dy
如果不懂,祝学习愉快!

dz=[2xy^2cos(x^2y^2)+3]dx+[2x^2ycos(x^2y^2)-10y]dy