We will find the function differential with the differential formula
dz=zx′dx+zy′dy
In the formula above we see the function partial derivatives. Hence, we calculate them.
zx′(x,y)=2xy4−3x2y3+4x3y2
zy′(x,y)=4y3x2−3y2x3+2yx4
Now, we put the derivatives in the formula and get
dz=zx′dx+zy′dy
dz=(2xy4−3x2y3+4x3y2)dx+(4y3x2−3y2x3+2yx4)dy
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