derivative \sqrt[3]{5+6x^6}

解答

导数

3 5 + 6 x^{6}

\frac{12 x ^{5}}{( 5 + 6 x ^{6} ) ^{\frac{2}{3}}}

求解步骤

\frac{d}{d x} (3 5 + 6 x^{6})

使用连锁律:

\frac{1}{3 ( 5 + 6 x ^{6} ) ^{\frac{2}{3}}} \frac{d}{d x} (5 + 6 x^{6})

= \frac{1}{3 ( 5 + 6 x ^{6} ) ^{\frac{2}{3}}} \frac{d}{d x} (5 + 6 x^{6})

\frac{d}{d x} (5 + 6 x^{6}) = 36 x^{5}

= \frac{1}{3 ( 5 + 6 x ^{6} ) ^{\frac{2}{3}}} \cdot 36 x^{5}

化简

\frac{1}{3 ( 5 + 6 x ^{6} ) ^{\frac{2}{3}}} \cdot 36 x^{5} : \frac{12 x ^{5}}{( 5 + 6 x ^{6} ) ^{\frac{2}{3}}}

= \frac{12 x ^{5}}{( 5 + 6 x ^{6} ) ^{\frac{2}{3}}}

\frac{\partial}{\partial x} (5 - x^{2} + x y - 2^{2})

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

x \to 0 + lim (6 - \frac{1}{x ^{2}})

d er i v a t i v e y = 4 x^{\frac{2}{3}} + 6 x^{\frac{1}{2}} - 8

\int 8 x + 3 d x