设参数方程{x=r^2cosθy=r^3sin2θ1,当r是常数,θ是参数时,dy/dx=2,当θ是常数,r是参数时,dy/dx=

Question

设参数方程{ x=r^2cosθ y=r^3sin2θ
1,当r是常数,θ是参数时,dy/dx=
2,当θ是常数,r是参数时,dy/dx=

Answer 1

1
dx/dθ=-r^2sinθ
dy/dθ=2r^3cos2θ
dy/dx=-2rcos2θ/sinθ
2
dx/dr=2rcosθ
dy/dr=3r^2sin2θ=6r^2sinθcosθ
dy/dx=3rsinθ