derivative y= 4/3 (x+1)^{3/2}

解答

导数

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

2 (x + 1)^{\frac{1}{2}}

求解步骤

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

将常数提出:

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

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

使用连锁律:

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

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

\frac{d}{d x} (x + 1) = 1

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

化简

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

= 2 (x + 1)^{\frac{1}{2}}

\int_{0}^{- 0.5} 150 x d x

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