dx/dt=-e⁻ᵗ
dy/dt=2e²ᵗ+4te²ᵗ
d²x/dt²=e⁻ᵗ
d²y/dt²=8e²ᵗ+8te²ᵗ
d²y/dx²=d/dx(dy/dx)
=d/dx[(dy/dt)/(dx/dt)]
=d/(dt·dx/dt)[(dy/dt)/(dx/dt)]
=[(d²y/dt²)·(dx/dt)-(dy/dt)·(d²x/dt²)/(dx/dt)³
=[(8e²ᵗ+8te²ᵗ)·(-e⁻ᵗ)-(2e²ᵗ+4te²ᵗ)·e⁻ᵗ]/-e⁻³ᵗ
=10e⁴ᵗ+12te⁴ᵗ
游客1
dx/dt=-e⁻ᵗ
dy/dt=2e²ᵗ+4te²ᵗ
d²x/dt²=e⁻ᵗ
d²y/dt²=8e²ᵗ+8te²ᵗ
d²y/dx²=d/dx(dy/dx)
=d/dx[(dy/dt)/(dx/dt)]
=d/(dt·dx/dt)[(dy/dt)/(dx/dt)]
=[(d²y/dt²)·(dx/dt)-(dy/dt)·(d²x/dt²)/(dx/dt)³
=[(8e²ᵗ+8te²ᵗ)·(-e⁻ᵗ)-(2e²ᵗ+4te²ᵗ)·e⁻ᵗ]/-e⁻³ᵗ
=10e⁴ᵗ+12te⁴ᵗ