derivative y=7(x^3+x^2) 2/3

解答

导数

y = 7 (x^{3} + x^{2}) \frac{2}{3}

14 x^{2} + \frac{28 x}{3}

求解步骤

\frac{d}{d x} (7 (x^{3} + x^{2}) \frac{2}{3})

化简

7 (x^{3} + x^{2}) \frac{2}{3} : \frac{14}{3} (x^{3} + x^{2})

= \frac{d}{d x} (\frac{14}{3} (x^{3} + x^{2}))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{14}{3} \frac{d}{d x} (x^{3} + x^{2})

使用微分加减法定则:

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

= \frac{14}{3} (\frac{d}{d x} (x^{3}) + \frac{d}{d x} (x^{2}))

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

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

= \frac{14}{3} (3 x^{2} + 2 x)

化简

\frac{14}{3} (3 x^{2} + 2 x) : 14 x^{2} + \frac{28 x}{3}

= 14 x^{2} + \frac{28 x}{3}

\frac{d}{d x} (10 (1. 1^{\frac{x}{2}}))

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