derivative of-(81/((1+9x)^2))

解答

\frac{d}{d x} (- \frac{81}{( 1 + 9 x ) ^{2}})

\frac{1458}{( 1 + 9 x ) ^{3}}

求解步骤

\frac{d}{d x} (- \frac{81}{( 1 + 9 x ) ^{2}})

将常数提出:

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

= - 81 \frac{d}{d x} (\frac{1}{( 1 + 9 x ) ^{2}})

使用指数法则:

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

= - 81 \frac{d}{d x} ((1 + 9 x)^{- 2})

使用连锁律:

- \frac{2}{( 1 + 9 x ) ^{3}} \frac{d}{d x} (1 + 9 x)

= - \frac{2}{( 1 + 9 x ) ^{3}} \frac{d}{d x} (1 + 9 x)

\frac{d}{d x} (1 + 9 x) = 9

= - 81 (- \frac{2}{( 1 + 9 x ) ^{3}} \cdot 9)

化简

- 81 (- \frac{2}{( 1 + 9 x ) ^{3}} \cdot 9) : \frac{1458}{( 1 + 9 x ) ^{3}}

= \frac{1458}{( 1 + 9 x ) ^{3}}

a re a y = 5 x^{2}, y = 30 x - 45, [0, 45]

d er i v a t i v e Y = Y = ln (x - 3)

\int sin (2 x) \cdot e^{x} d x

\int_{0}^{\frac{1}{5}} 2 arcsin (5 y) d y

d er i v a t i v e f (x) = sin (x) csc (x)