derivative 1/(4x-3)

解答

导数

\frac{1}{4 x - 3}

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

求解步骤

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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

\int_{7}^{9} (x^{2} + 2 x - 4) d x

\int \frac{tan ( z )}{cos ^{2} ( z )} d z

x \to 1 + lim (\frac{4 x - 3}{x - 1})

\frac{d}{d x} (x^{7} + \frac{1}{x ^{7}} + 7 x + \frac{7}{x} + 7)

\frac{d y}{d t} - 2 y = e^{2 t}