derivative of \sqrt[3]{x^2}+5sqrt(x^3)

解答

\frac{d}{d x} (3 x^{2} + 5 x^{3})

\frac{4 + 45 x ^{\frac{5}{6}}}{6 3 x}

求解步骤

\frac{d}{d x} (3 x^{2} + 5 x^{3})

使用微分加减法定则:

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

= \frac{d}{d x} (3 x^{2}) + \frac{d}{d x} (5 x^{3})

\frac{d}{d x} (3 x^{2}) = \frac{2}{3 x ^{\frac{1}{3}}}

\frac{d}{d x} (5 x^{3}) = \frac{15 x}{2}

= \frac{2}{3 x ^{\frac{1}{3}}} + \frac{15 x}{2}

化简

\frac{2}{3 x ^{\frac{1}{3}}} + \frac{15 x}{2} : \frac{4 + 45 x ^{\frac{5}{6}}}{6 3 x}

= \frac{4 + 45 x ^{\frac{5}{6}}}{6 3 x}

a re a 6 x - x^{2}, 0, 6

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