derivative 1500x+3000(4x+3)^{-1}-1000

解答

导数

1500 x + 3000 (4 x + 3)^{- 1} - 1000

- \frac{12000}{( 4 x + 3 ) ^{2}} + 1500

求解步骤

\frac{d}{d x} (1500 x + 3000 (4 x + 3)^{- 1} - 1000)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (1500 x) + \frac{d}{d x} (3000 (4 x + 3)^{- 1}) - \frac{d}{d x} (1000)

\frac{d}{d x} (1500 x) = 1500

\frac{d}{d x} (3000 (4 x + 3)^{- 1}) = - \frac{12000}{( 4 x + 3 ) ^{2}}

\frac{d}{d x} (1000) = 0

= 1500 - \frac{12000}{( 4 x + 3 ) ^{2}} - 0

化简

= - \frac{12000}{( 4 x + 3 ) ^{2}} + 1500

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