derivative f(x)= 4/((3x)^{-2)}

解答

导数

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

72 x

求解步骤

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

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

2 \cdot 3 x \frac{d}{d x} (3 x)

= 2 \cdot 3 x \frac{d}{d x} (3 x)

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

= 4 \cdot 2 \cdot 3 x \cdot 3

化简

= 72 x

\int \frac{5}{x ^{- 1} + 5} d x

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