Question

已知参数方程x=t+t^2,y=cost.求导数dy/dx和d^2y/dx^2

Answer 1

x=t+t^2,y=cost

所以

dx/dt=1+2t,dy/dt= -sint

于是

dy/dx=(dy/dt) / (dx/dt)= -sint/(1+2t)

而

d^2y/dx^2

=(dy/dx)/dt *dt/dx

=[-sint/(1+2t)]' /(1+2t)

=[-cost*(1+2t)+2sint]/(1+2t)^3