derivative y=(2/((2x-6) 3/2))

解答

导数

y = (\frac{2}{( 2 x - 6 ) \frac{3}{2}})

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

求解步骤

\frac{d}{d x} (\frac{2}{( 2 x - 6 ) \frac{3}{2}})

将常数提出:

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

= \frac{2}{\frac{3}{2}} \frac{d}{d x} (\frac{1}{2 x - 6})

使用指数法则:

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

= \frac{2}{\frac{3}{2}} \frac{d}{d x} ((2 x - 6)^{- 1})

使用连锁律:

- \frac{1}{( 2 x - 6 ) ^{2}} \frac{d}{d x} (2 x - 6)

= - \frac{1}{( 2 x - 6 ) ^{2}} \frac{d}{d x} (2 x - 6)

\frac{d}{d x} (2 x - 6) = 2

= \frac{2}{\frac{3}{2}} (- \frac{1}{( 2 x - 6 ) ^{2}} \cdot 2)

化简

\frac{2}{\frac{3}{2}} (- \frac{1}{( 2 x - 6 ) ^{2}} \cdot 2) : - \frac{2}{3 ( x - 3 ) ^{2}}

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

t an g e n t - sin (\frac{x}{2})

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