(\partial)/(\partial x)((3y)*(2x)^{-1})

解答

\frac{\partial}{\partial x} ((3 y) \cdot (2 x)^{- 1})

- \frac{3 y}{2 x ^{2}}

求解步骤

\frac{\partial}{\partial x} ((3 y) (2 x)^{- 1})

将

y

视为常数

将常数提出:

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

= 3 y \frac{\partial}{\partial x} ((2 x)^{- 1})

使用连锁律:

- \frac{1}{( 2 x ) ^{2}} \frac{\partial}{\partial x} (2 x)

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

\frac{\partial}{\partial x} (2 x) = 2

= 3 y (- \frac{1}{( 2 x ) ^{2}} \cdot 2)

化简

3 y (- \frac{1}{( 2 x ) ^{2}} \cdot 2) : - \frac{3 y}{2 x ^{2}}

= - \frac{3 y}{2 x ^{2}}

p a r i t y f (x) = sin (tan (2 x))

d er i v a t i v e 2 (2 x^{5} - 3 x + 2)^{8}

\int 3 x y

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

\int (t + 7) e^{2 t + 3} d t