问题标题:
x=f'(t)且y=tf'(t)-f(t)设f''(x)存在且不为零.求f''(x)
问题描述:
x=f'(t)且y=tf'(t)-f(t)设f''(x)存在且不为零.求f''(x)
汪审权回答:
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)
f''(x)=1/f''(t)
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