Question

x=lnsint y=cost+tsint的二阶导数d^2y/dx^2

Answer 1

解题须知:

dy/dx = y'(t) / x'(t)

设:

z = dy/dx

z

= dy/dx

= y'(t) / x'(t)

= t Cos(t) / Cot(t)

= t Sin(t)

dz/dx

= z'(t) / x'(t)

= (t Cos(t) + Sin(t)) / Cot(t)

= Sin(t) (t + Tan(t))

所以 d^2y/dx^2 = Sin(t) (t + Tan(t))