y=x^(1/3)求导
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y=x^(1/3)求导
要用(f(x)-f(a))/x-a求
要用(f(x)-f(a))/x-a求
![y=x^(1/3)求导](/uploads/image/z/17658911-47-1.jpg?t=y%3Dx%5E%281%2F3%29%E6%B1%82%E5%AF%BC)
x-a=[x^(1/3)-a^(1/3)][x^(2/3)+x^(1/3)a^(1/3)+a^(2/3)]
所以f'(a)=lim(x趋于a)(f(x)-f(a))/x-a
=lim(x趋于a)1/[x^(2/3)+x^(1/3)a^(1/3)+a^(2/3)]
=1/(3*a^(2/3))
=1/2*a^(-2/3)
所以f'(a)=lim(x趋于a)(f(x)-f(a))/x-a
=lim(x趋于a)1/[x^(2/3)+x^(1/3)a^(1/3)+a^(2/3)]
=1/(3*a^(2/3))
=1/2*a^(-2/3)