derivative y= 4/3 (2x-1)^3

解答

导数

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

8 (2 x - 1)^{2}

求解步骤

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

将常数提出:

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

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

使用连锁律:

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

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

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

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

化简

\frac{4}{3} \cdot 3 (2 x - 1)^{2} \cdot 2 : 8 (2 x - 1)^{2}

= 8 (2 x - 1)^{2}

d er i v a t i v e x^{2} + 16

d er i v a t i v e y = 2 x^{3} - x^{2} + 2

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

d er i v a t i v e - 2 e^{- 2 x}

\int \frac{3 x ^{3} - 4 x - 2}{x ^{3}} d x