Find

Question

dy/dx and d2y/dx2.
x = e^t, y = te^t

Answer 1

x=e^t
dx/dt=e^t

y=te^t
dy/dt=e^t+te^t

dy/dx=dy/dt / dx/dt=(e^t)/(e^t(1+t))= 1/(1+t)

y"/dx"=D (1/(1+t)=-1/(1+t)^2

Answer 2

not so. you have found d/dt (dy/dx), but you want

d/dx (dy/dx) = d/dt(dy/dx) / dx/dt
= -1/(1+t)^2 / e^t = -1/((1+t)^2 e^t)