derivative of (x^3/3+(x^2)/2-6x)

解答

\frac{d}{d x} (\frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 6 x)

x^{2} + x - 6

求解步骤

\frac{d}{d x} (\frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 6 x)

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{x ^{3}}{3}) + \frac{d}{d x} (\frac{x ^{2}}{2}) - \frac{d}{d x} (6 x)

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

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

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

= x^{2} + x - 6

\frac{d}{d x} (2 e^{x^{2}})

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\int \frac{1}{P} d P

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