derivative sqrt(1-x^{12)}

解答

导数

1 - x^{12}

- \frac{6 x ^{11}}{1 - x ^{12}}

求解步骤

\frac{d}{d x} (1 - x^{12})

使用连锁律:

\frac{1}{2 1 - x ^{12}} \frac{d}{d x} (1 - x^{12})

= \frac{1}{2 1 - x ^{12}} \frac{d}{d x} (1 - x^{12})

\frac{d}{d x} (1 - x^{12}) = - 12 x^{11}

= \frac{1}{2 1 - x ^{12}} (- 12 x^{11})

化简

\frac{1}{2 1 - x ^{12}} (- 12 x^{11}) : - \frac{6 x ^{11}}{1 - x ^{12}}

= - \frac{6 x ^{11}}{1 - x ^{12}}

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