derivative of 15x^5-(60/(7x^6)-1)

解答

\frac{d}{d x} (15 x^{5} - \frac{60}{7 x ^{6}} - 1)

75 x^{4} + \frac{360}{7 x ^{7}}

求解步骤

\frac{d}{d x} (15 x^{5} - \frac{60}{7 x ^{6}} - 1)

使用微分加减法定则:

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

= \frac{d}{d x} (15 x^{5}) - \frac{d}{d x} (\frac{60}{7 x ^{6}}) - \frac{d}{d x} (1)

\frac{d}{d x} (15 x^{5}) = 75 x^{4}

\frac{d}{d x} (\frac{60}{7 x ^{6}}) = - \frac{360}{7 x ^{7}}

\frac{d}{d x} (1) = 0

= 75 x^{4} - (- \frac{360}{7 x ^{7}}) - 0

化简

= 75 x^{4} + \frac{360}{7 x ^{7}}

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