derivative x^{2020}+1/3 x^3-4x^2

解答

导数

x^{2020} + \frac{1}{3} x^{3} - 4 x^{2}

2020 x^{2019} + x^{2} - 8 x

求解步骤

\frac{d}{d x} (x^{2020} + \frac{1}{3} x^{3} - 4 x^{2})

化简

x^{2020} + \frac{1}{3} x^{3} - 4 x^{2} : x^{2020} + \frac{x ^{3}}{3} - 4 x^{2}

= \frac{d}{d x} (x^{2020} + \frac{x ^{3}}{3} - 4 x^{2})

使用微分加减法定则:

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

= \frac{d}{d x} (x^{2020}) + \frac{d}{d x} (\frac{x ^{3}}{3}) - \frac{d}{d x} (4 x^{2})

\frac{d}{d x} (x^{2020}) = 2020 x^{2019}

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

\frac{d}{d x} (4 x^{2}) = 8 x

= 2020 x^{2019} + x^{2} - 8 x

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