derivative of 1/(1+x^3)

解答

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

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

求解步骤

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

使用指数法则:

\frac{1}{a} = a^{- 1}

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

使用连锁律:

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

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

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

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

化简

- \frac{1}{( 1 + x ^{3} ) ^{2}} \cdot 3 x^{2} : - \frac{3 x ^{2}}{( 1 + x ^{3} ) ^{2}}

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

\int \frac{x ^{2} - x + 24}{x ^{3} + 6 x} d x

t an g e n t y = x - 3 x^{2}, (3, - 24)

\frac{\partial}{\partial x} (3 x^{2} y^{4} - 2)

\int (5 x - 7) e^{5 x - 7} d x

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