derivative of (4x^{3/2}-2x^{1/2}^3)

解答

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

\frac{3 ( - 1 + 6 x ) ( 4 x ^{\frac{3}{2}} - 2 x ^{\frac{1}{2}} ) ^{2}}{x ^{\frac{1}{2}}}

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}}) = \frac{- 1 + 6 x}{x ^{\frac{1}{2}}}

= 3 (4 x^{\frac{3}{2}} - 2 x^{\frac{1}{2}})^{2} \frac{- 1 + 6 x}{x ^{\frac{1}{2}}}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 ( - 1 + 6 x ) ( 4 x ^{\frac{3}{2}} - 2 x ^{\frac{1}{2}} ) ^{2}}{x ^{\frac{1}{2}}}

\int tan (2 x) sec^{5} (2 x) d x

\frac{d}{d x} ((\frac{4}{5} x)^{4})

\int 4 sec^{2} (2 x) tan (2 x) d x

d er i v a t i v e 100 - h^{2}

\frac{d}{d x} ((a - x)^{2})