derivative y=5e^x+2/(\sqrt[3]{x)}

解答

导数

y = 5 e^{x} + \frac{2}{3 x}

5 e^{x} - \frac{2}{3 x ^{\frac{4}{3}}}

求解步骤

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

使用微分加减法定则:

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

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

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

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

= 5 e^{x} - \frac{2}{3 x ^{\frac{4}{3}}}

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