x=1-t^2y=t-t^3求d^3y/dx^3=?要理论...三阶导数公式是什么,怎么推导啊?

Answer 1

dy/dx=(1-3t²)/(-2t)=(3t²-1)/(2t)=(3/2)t-(1/2)(1/t)
下同计算的整个思路就是,只要是对 t 求完导,都要乘以(dt/dx),也就是除以(dx/dt)
d²y/dx²=[d(dy/dx)/dt](dt/dx)
=[d(dy/dx)/dt] / (dx/dt)
=[3/2 + (1/2)(1/t²)]/(-2t)
=-(3/4)(1/t) - (1/4)(1/t³)
d³y/dx³=[-(3/4)(1/t) - (1/4)(1/t³)]' / (dx/dt)
=[(3/4)(1/t²) + (1/12)(1/t^4)] / (-2t)
=-(3/8)(1/t³) - (1/24)(1/t^5)

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