derivative a/x

解答

导数

\frac{a}{x}

- \frac{a}{x ^{2}}

求解步骤

\frac{d}{d x} (\frac{a}{x})

将常数提出:

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

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

使用指数法则:

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

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

使用幂法则:

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

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

化简

a (- 1 \cdot x^{- 1 - 1}) : - \frac{a}{x ^{2}}

= - \frac{a}{x ^{2}}

in v erse l a pl a ce \frac{s}{( s - 1 )}

y (1 + x^{2}) y^{^{'}} - x (6 + y^{2}) = 0

d er i v a t i v e y = 5 x^{4} e^{x} + e^{x} x^{5}

x \to 1 lim (- 6 + 2 x^{2})

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