derivative f(x)=16x^{1/8}

解答

导数

f (x) = 16 x^{\frac{1}{8}}

\frac{2}{x ^{\frac{7}{8}}}

求解步骤

\frac{d}{d x} (16 x^{\frac{1}{8}})

将常数提出:

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

= 16 \frac{d}{d x} (x^{\frac{1}{8}})

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 16 \cdot \frac{1}{8} x^{\frac{1}{8} - 1}

化简

16 \cdot \frac{1}{8} x^{\frac{1}{8} - 1} : \frac{2}{x ^{\frac{7}{8}}}

= \frac{2}{x ^{\frac{7}{8}}}

y^{^{''}} - 4 y^{^{'}} + 4 y = (12 x^{2} - 6 x) e^{2 x}

\int \frac{( 12 x + 30 )}{x ^{2} + 2 x - 8} d x

\int_{1}^{2} \frac{4 y ^{2} - 6 y - 12}{y ( y + 2 ) ( y - 3 )} d y

\int x^{2} sinh (x) d x

d er i v a t i v e f (x) = 2 x^{- 2} - 3 x^{- \frac{7}{3}}