x=f(t)

y=g(t)

y'=g'(t)/f'(t)

y''=y'|'t/x'|t

=[g'(t)/f'(t)]'|t//f'(t)

=[g''(t)f'(t)-g'(t)f''(t)]/[f'(t)]^2

y'''=y''|'t/x'|t

={[g''(t)f'(t)-g'(t)f''(t)]/[f'(t)]^2}‘|t//x'|t

={[g''(t)f'(t)-g'(t)f''(t)]'|t*[f'(t)]^2-[g''(t)f'(t)-g'(t)f''(t)]*2f'(t)*f''(t)}/[f'(t)]^5

={[g'''(t)f'(t)+g''(t)f''(t)-g''(t)f''(t)-g'(t)f'''(t)]*[f'(t)]^2-[g''(t)f'(t)-g'(t)f''(t)]*2f'(t)*f''(t)}/[f'(t)]^5

={[g'''(t)f'(t)-g'(t)f'''(t)]*[f'(t)]-2[g''(t)f'(t)-g'(t)f''(t)]f''(t)}/[f'(t)]^4