derivative of (54/((1+3x)^3))

解答

\frac{d}{d x} (\frac{54}{( 1 + 3 x ) ^{3}})

- \frac{486}{( 1 + 3 x ) ^{4}}

求解步骤

\frac{d}{d x} (\frac{54}{( 1 + 3 x ) ^{3}})

将常数提出:

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

= 54 \frac{d}{d x} (\frac{1}{( 1 + 3 x ) ^{3}})

使用指数法则:

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

= 54 \frac{d}{d x} ((1 + 3 x)^{- 3})

使用连锁律:

- \frac{3}{( 1 + 3 x ) ^{4}} \frac{d}{d x} (1 + 3 x)

= - \frac{3}{( 1 + 3 x ) ^{4}} \frac{d}{d x} (1 + 3 x)

\frac{d}{d x} (1 + 3 x) = 3

= 54 (- \frac{3}{( 1 + 3 x ) ^{4}} \cdot 3)

化简

54 (- \frac{3}{( 1 + 3 x ) ^{4}} \cdot 3) : - \frac{486}{( 1 + 3 x ) ^{4}}

= - \frac{486}{( 1 + 3 x ) ^{4}}

y^{^{'}} = (1 - 2 t) y

t an g e n t \frac{x ^{2}}{x - 6}

\frac{d}{d x} (\frac{2 cos ( 2 x ) - 1}{2 cos ( x )})

\frac{\partial}{\partial y} (1 + e^{x} y + x e^{x} y)

y^{^{''}} - 6 y^{^{'}} + 9 y = t^{- 4} e^{3 t}