derivative of x^6-3x^5+10x^3-15x^2+9x-2

解答

\frac{d}{d x} (x^{6} - 3 x^{5} + 10 x^{3} - 15 x^{2} + 9 x - 2)

6 x^{5} - 15 x^{4} + 30 x^{2} - 30 x + 9

求解步骤

\frac{d}{d x} (x^{6} - 3 x^{5} + 10 x^{3} - 15 x^{2} + 9 x - 2)

使用微分加减法定则:

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

= \frac{d}{d x} (x^{6}) - \frac{d}{d x} (3 x^{5}) + \frac{d}{d x} (10 x^{3}) - \frac{d}{d x} (15 x^{2}) + \frac{d}{d x} (9 x) - \frac{d}{d x} (2)

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

\frac{d}{d x} (3 x^{5}) = 15 x^{4}

\frac{d}{d x} (10 x^{3}) = 30 x^{2}

\frac{d}{d x} (15 x^{2}) = 30 x

\frac{d}{d x} (9 x) = 9

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

= 6 x^{5} - 15 x^{4} + 30 x^{2} - 30 x + 9 - 0

化简

= 6 x^{5} - 15 x^{4} + 30 x^{2} - 30 x + 9

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