\[\begin{aligned} d f &=d^{1} f=\frac{\partial f}{\partial x} d x+\frac{\partial f}{\partial y} d y \\ &=\sin y d x+x \cos y d y; \\ d^{2} f &=\frac{\partial^{2} f}{\partial x^{2}} d x^{2}+2 \frac{\pa...df=d1f=∂f∂xdx+∂f∂ydy=sinydx+xcosydy;d2f=∂2f∂x2dx2+2∂2f∂x∂ydxdy+∂2f∂y2dy2=2cosydxdy−xsinydy2;d3f=−3sinydxdy2−xcosydy3;
