Question

50 баллов,очень надо(( найти dy/dx и d^2y/dx^2 для функции, заданной параметрически: x= t-sint y= 1-cost

Answer 1

Dy/dx = dy/dt · dt/dx = dy/dt : dx/dt
dy/dt = sint
dx/dt = 1 - cost
dy/dx = sint/(1-cost)
d²y/dx² = d/dx(dy/dx) = d/dt(dy/dx) : dx/dt
d/dt(dy/dx) = (cost(1-cost) - sin²t)/(1 - cost)²
d²y/dx² = (cost(1-cost) - sin²t)(1 - cost)/[(1 - cost)² sint] =
= (cost - cos²t -sin²t)/sint = (cost - 1)/sint
d²y/dx²  = (cost - 1)/sint