derivative of 1/((1-2x^{3/2)})

解答

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

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

求解步骤

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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

\frac{\partial}{\partial x} (x^{\frac{2}{3}} + y^{\frac{2}{3}})

\int \frac{1}{64 + x ^{2}} d x

f (x) = x cos (x)

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

t a y l or \frac{1}{1 + x ^{2}}, 0