derivative of 8sqrt(x)+6x^{3/4}

解答

\frac{d}{d x} (8 x + 6 x^{\frac{3}{4}})

\frac{4}{x ^{\frac{1}{2}}} + \frac{9}{2 x ^{\frac{1}{4}}}

求解步骤

\frac{d}{d x} (8 x + 6 x^{\frac{3}{4}})

使用微分加减法定则:

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

= \frac{d}{d x} (8 x) + \frac{d}{d x} (6 x^{\frac{3}{4}})

\frac{d}{d x} (8 x) = \frac{4}{x ^{\frac{1}{2}}}

\frac{d}{d x} (6 x^{\frac{3}{4}}) = \frac{9}{2 x ^{\frac{1}{4}}}

= \frac{4}{x ^{\frac{1}{2}}} + \frac{9}{2 x ^{\frac{1}{4}}}

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