derivative ((sqrt(x))/3+9)^{3/2}

解答

导数

(\frac{x}{3} + 9)^{\frac{3}{2}}

\frac{( x + 27 ) ^{\frac{1}{2}}}{4 \cdot 3 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

求解步骤

\frac{d}{d x} ((\frac{x}{3} + 9)^{\frac{3}{2}})

化简

(\frac{x}{3} + 9)^{\frac{3}{2}} : (\frac{x + 27}{3})^{\frac{3}{2}}

= \frac{d}{d x} ((\frac{x + 27}{3})^{\frac{3}{2}})

使用连锁律:

\frac{3 ( \frac{x + 27}{3} ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (\frac{x + 27}{3})

= \frac{3 ( \frac{x + 27}{3} ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (\frac{x + 27}{3})

\frac{d}{d x} (\frac{x + 27}{3}) = \frac{1}{6 x ^{\frac{1}{2}}}

= \frac{3 ( \frac{x + 27}{3} ) ^{\frac{1}{2}}}{2} \cdot \frac{1}{6 x ^{\frac{1}{2}}}

化简

\frac{3 ( \frac{x + 27}{3} ) ^{\frac{1}{2}}}{2} \cdot \frac{1}{6 x ^{\frac{1}{2}}} : \frac{( x + 27 ) ^{\frac{1}{2}}}{4 \cdot 3 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

= \frac{( x + 27 ) ^{\frac{1}{2}}}{4 \cdot 3 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

\int_{0}^{- 1} \frac{x ^{3} + 8}{x + 2} d x

\frac{d y}{d x} + \frac{y}{x} = x^{3} y^{2}

\frac{d}{d x} (ln e^{1 + x^{2}} + 3 x^{4} + cot^{2} (π x))

(\frac{1}{1 + e ^{- x}})^{^{'}}

p a r i t y \frac{tan ( x )}{x}