derivative of x^{1/11}(x-1^2)

解

\frac{d}{d x} (x^{\frac{1}{11}} (x - 1)^{2})

\frac{23 x ^{2} - 24 x + 1}{11 x ^{\frac{10}{11}}}

解答ステップ

\frac{d}{d x} (x^{\frac{1}{11}} (x - 1)^{2})

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{\frac{1}{11}}, g = (x - 1)^{2}

= \frac{d}{d x} (x^{\frac{1}{11}}) (x - 1)^{2} + \frac{d}{d x} ((x - 1)^{2}) x^{\frac{1}{11}}

\frac{d}{d x} (x^{\frac{1}{11}}) = \frac{1}{11 x ^{\frac{10}{11}}}

\frac{d}{d x} ((x - 1)^{2}) = 2 (x - 1)

= \frac{1}{11 x ^{\frac{10}{11}}} (x - 1)^{2} + 2 (x - 1) x^{\frac{1}{11}}

簡素化

\frac{1}{11 x ^{\frac{10}{11}}} (x - 1)^{2} + 2 (x - 1) x^{\frac{1}{11}} : \frac{23 x ^{2} - 24 x + 1}{11 x ^{\frac{10}{11}}}

= \frac{23 x ^{2} - 24 x + 1}{11 x ^{\frac{10}{11}}}