derivative of (10/((x+5)^2))

解答

\frac{d}{d x} (\frac{10}{( x + 5 ) ^{2}})

- \frac{20}{( x + 5 ) ^{3}}

求解步骤

\frac{d}{d x} (\frac{10}{( x + 5 ) ^{2}})

将常数提出:

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

= 10 \frac{d}{d x} (\frac{1}{( x + 5 ) ^{2}})

使用指数法则:

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

= 10 \frac{d}{d x} ((x + 5)^{- 2})

使用连锁律:

- \frac{2}{( x + 5 ) ^{3}} \frac{d}{d x} (x + 5)

= - \frac{2}{( x + 5 ) ^{3}} \frac{d}{d x} (x + 5)

\frac{d}{d x} (x + 5) = 1

= 10 (- \frac{2}{( x + 5 ) ^{3}} \cdot 1)

化简

10 (- \frac{2}{( x + 5 ) ^{3}} \cdot 1) : - \frac{20}{( x + 5 ) ^{3}}

= - \frac{20}{( x + 5 ) ^{3}}

t a y l or x \cdot sin (x)

\int \frac{3 ( - 5 + ln ( 4 x ) ) ^{3}}{x} d x

t an g e n t f (x) = x^{2} - 9 x + 18, 4, at x = 3

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t an g e n t f (x) = \frac{3}{x + 3}, at x = - \frac{1}{3}