Question

高等数学如图第三小题

Answer 1

1. xy-lny=e

   y+xy'-y'/y=0→y²+xyy'-y'=0→dy/dx=y²/(1-xy)

2. √(x²+y²)=arctan(y/x)

   (2x+2y·y')/2√(x²+y²)=(y/x)'/(1+y²/x²)=[y'x-y]/(x²+y²)

   (x+y·y')√(x²+y²)=y'x-y→dy/dx=[y+x√(x²+y²)]/x-y√(x²+y²)]

3. sin(xy)+cos(xz)+tan(yz)=0

   cos(xy)·y-sin(xz)·(z+x∂z/∂x)+sec²(yz)·y·∂z/∂x→

   ∂z/∂x=[ycos(xy)-zsin(xz)]/[xsin(xz)-ysec²(yz)

   cos(xy)·x-xcos(xz)∂z/∂y+sec²(yz)·(z+∂z/∂y)→