derivative of 2x^6-8x^5+10x^4-10x^2+8x-2

解答

\frac{d}{d x} (2 x^{6} - 8 x^{5} + 10 x^{4} - 10 x^{2} + 8 x - 2)

12 x^{5} - 40 x^{4} + 40 x^{3} - 20 x + 8

求解步骤

\frac{d}{d x} (2 x^{6} - 8 x^{5} + 10 x^{4} - 10 x^{2} + 8 x - 2)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x^{6}) - \frac{d}{d x} (8 x^{5}) + \frac{d}{d x} (10 x^{4}) - \frac{d}{d x} (10 x^{2}) + \frac{d}{d x} (8 x) - \frac{d}{d x} (2)

\frac{d}{d x} (2 x^{6}) = 12 x^{5}

\frac{d}{d x} (8 x^{5}) = 40 x^{4}

\frac{d}{d x} (10 x^{4}) = 40 x^{3}

\frac{d}{d x} (10 x^{2}) = 20 x

\frac{d}{d x} (8 x) = 8

\frac{d}{d x} (2) = 0

= 12 x^{5} - 40 x^{4} + 40 x^{3} - 20 x + 8 - 0

化简

= 12 x^{5} - 40 x^{4} + 40 x^{3} - 20 x + 8

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