derivative of (10/(x-6))

解答

\frac{d}{d x} (\frac{10}{x - 6})

- \frac{10}{( x - 6 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{10}{x - 6})

将常数提出:

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

= 10 \frac{d}{d x} (\frac{1}{x - 6})

使用指数法则:

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

= 10 \frac{d}{d x} ((x - 6)^{- 1})

使用连锁律:

- \frac{1}{( x - 6 ) ^{2}} \frac{d}{d x} (x - 6)

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

\frac{d}{d x} (x - 6) = 1

= 10 (- \frac{1}{( x - 6 ) ^{2}} \cdot 1)

化简

10 (- \frac{1}{( x - 6 ) ^{2}} \cdot 1) : - \frac{10}{( x - 6 ) ^{2}}

= - \frac{10}{( x - 6 ) ^{2}}

f (x) = \frac{x}{x ^{2} - x + 1}

x \to 0 + lim (x \cdot sin (\frac{1}{x}))

(3 sin (x))^{^{'}}

a re a f (x) = 2 sin (x), g (x) = 2 cos (x)

x \to 0 + lim (5 x + 9)