derivative 1/(2x+1)

解答

导数

\frac{1}{2 x + 1}

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

求解步骤

\frac{d}{d x} (\frac{1}{2 x + 1})

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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

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

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

\int (15 x^{13}) d x

\int 9 x^{2} - 4 x + 3 d x

p \to 4 lim (p^{2} + p + 5)