derivative of 4\sqrt[3]{x^7}-1/(x^2+2x)

解答

\frac{d}{d x} (4 3 x^{7} - \frac{1}{x ^{2}} + 2 x)

\frac{28 x ^{\frac{13}{3}} + 6}{3 x ^{3}} + 2

求解步骤

\frac{d}{d x} (4 3 x^{7} - \frac{1}{x ^{2}} + 2 x)

使用微分加减法定则:

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

= \frac{d}{d x} (4 3 x^{7}) - \frac{d}{d x} (\frac{1}{x ^{2}}) + \frac{d}{d x} (2 x)

\frac{d}{d x} (4 3 x^{7}) = \frac{28 x ^{\frac{4}{3}}}{3}

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

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

= \frac{28 x ^{\frac{4}{3}}}{3} - (- \frac{2}{x ^{3}}) + 2

化简

\frac{28 x ^{\frac{4}{3}}}{3} - (- \frac{2}{x ^{3}}) + 2 : \frac{28 x ^{\frac{13}{3}} + 6}{3 x ^{3}} + 2

= \frac{28 x ^{\frac{13}{3}} + 6}{3 x ^{3}} + 2

t an g e n t 7 x - 7 x

\frac{d}{d x} ((\frac{4 x + 1}{2 - 5 x})^{\frac{1}{3}})

d er i v a t i v e f (x) = 5 x^{2} cos (x) - 4 x

d er i v a t i v e y = arccos (2 x + 3)

in v erse l a pl a ce \frac{1}{( s + 1 ) ( s - 1 ) ^{2}}