derivative f(x)=(sqrt(5))/(x^6)

解答

导数

f (x) = \frac{5}{x ^{6}}

- \frac{6 5}{x ^{7}}

求解步骤

\frac{d}{d x} (\frac{5}{x ^{6}})

将常数提出:

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

= 5 \frac{d}{d x} (\frac{1}{x ^{6}})

使用指数法则:

\frac{1}{a} = a^{- 1}

= 5 \frac{d}{d x} (x^{- 6})

使用幂法则:

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

= 5 (- 6 x^{- 6 - 1})

化简

5 (- 6 x^{- 6 - 1}) : - \frac{6 5}{x ^{7}}

= - \frac{6 5}{x ^{7}}

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

\frac{( 1 + x ^{2} ) d y}{d x} - (1 + y^{2}) = 0

\int_{0}^{N} e^{- s t} e^{- 5 t} d t

\frac{y d y + x d x}{2 1 + x y} = 0

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 5)^{6})