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  • x=f'(t) y=tf'(t)-f(t)的三階導(dǎo)數(shù)?

    x=f'(t) y=tf'(t)-f(t)的三階導(dǎo)數(shù)?
    二階已知為1/f"(t)
    數(shù)學(xué)人氣:780 ℃時(shí)間:2020-01-25 07:06:53
    優(yōu)質(zhì)解答
    x=f'(t)
    y=tf'(t)-f(t)
    dy/dx
    =[dy/dt]/[dx/dt]
    =[f'(t)+tf''(t)-f'(t)]/f''(t)
    =t
    d^2y/dx^2
    =[d(dy/dx)/dt]/[dx/dt]
    =1/f''(t)
    d^3y/dx^3
    =[d(d^2y)/dt]/[dx/dt]
    =[d(1/f''(t))/dt]/f''(t)
    =[-f'''(t)/(f''(t))^2]/f''(t)
    =-f'''(t)/[f''(t)]^3
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