(\partial)/(\partial y)((2x)/((2x+3y)^2))

解答

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

- \frac{12 x}{( 2 x + 3 y ) ^{3}}

求解步骤

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

将

x

视为常数

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

\frac{\partial}{\partial y} (2 x + 3 y) = 3

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

化简

2 x (- \frac{2}{( 2 x + 3 y ) ^{3}} \cdot 3) : - \frac{12 x}{( 2 x + 3 y ) ^{3}}

= - \frac{12 x}{( 2 x + 3 y ) ^{3}}

d er i v a t i v e f (x) = e^{t}

t an g e n t y = 2 x + 1, (4, 3)

\int \frac{x ^{2}}{e ^{\frac{x}{3}}} d x

l a pl a ce t r an s f or m 5 \cdot t

\int \frac{1}{x ^{2} x ^{2} + 25} d x