derivative \sqrt[4]{(4x)/(4x-3)}

解答

导数

4 \frac{4 x}{4 x - 3}

- \frac{3}{2 2 x ^{\frac{3}{4}} ( 4 x - 3 ) ^{\frac{5}{4}}}

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (\frac{4 x}{4 x - 3}) = - \frac{12}{( 4 x - 3 ) ^{2}}

= \frac{1}{4 ( \frac{4 x}{4 x - 3} ) ^{\frac{3}{4}}} (- \frac{12}{( 4 x - 3 ) ^{2}})

化简

\frac{1}{4 ( \frac{4 x}{4 x - 3} ) ^{\frac{3}{4}}} (- \frac{12}{( 4 x - 3 ) ^{2}}) : - \frac{3}{2 2 x ^{\frac{3}{4}} ( 4 x - 3 ) ^{\frac{5}{4}}}

= - \frac{3}{2 2 x ^{\frac{3}{4}} ( 4 x - 3 ) ^{\frac{5}{4}}}

\frac{\partial}{\partial x} (ln (\frac{x}{y}))

\int_{- a}^{a} e^{\frac{- x ^{2}}{a ^{2}}} d x

s l o p e (- 4, 3), (3, 1)

\int \frac{x ^{2} - 15}{x + 7} d x

y^{^{''}} - 2 y^{^{'}} = 9 x