derivative of 1/(3x-4)

解答

\frac{d}{d x} (\frac{1}{3 x - 4})

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

求解步骤

\frac{d}{d x} (\frac{1}{3 x - 4})

使用指数法则:

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

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

使用连锁律:

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

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

\frac{d}{d x} (3 x - 4) = 3

= - \frac{1}{( 3 x - 4 ) ^{2}} \cdot 3

化简

- \frac{1}{( 3 x - 4 ) ^{2}} \cdot 3 : - \frac{3}{( 3 x - 4 ) ^{2}}

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

\frac{d}{d x} (2.2716 e^{0.2865 x})

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

d er i v a t i v e \frac{4 x + 1}{x}

\frac{d y}{d x} = \frac{x}{1 + x ^{2}}

x \to 3 lim (3 x - 3)