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

解

導関数

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

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

解答ステップ

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

和/差の法則を適用:

(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

簡素化

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