derivative of-3/(1-3x)

解答

\frac{d}{d x} (- \frac{3}{1 - 3 x})

- \frac{9}{( 1 - 3 x ) ^{2}}

求解步骤

\frac{d}{d x} (- \frac{3}{1 - 3 x})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

- 3 (- \frac{1}{( 1 - 3 x ) ^{2}} (- 3)) : - \frac{9}{( 1 - 3 x ) ^{2}}

= - \frac{9}{( 1 - 3 x ) ^{2}}

\int \frac{6000}{6 x + 70} d x

d er i v a t i v e y = \frac{x}{x + \frac{b}{x}}

t a y l or \frac{1}{( 1 + x ) ^{3}}, 0

in v erse l a pl a ce \frac{3}{s ^{2} + 9}

t an g e n t h (x) = \frac{9}{x}, at x = 2