(\partial)/(\partial x)(4/(4x+y))

解答

\frac{\partial}{\partial x} (\frac{4}{4 x + y})

- \frac{16}{( 4 x + y ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{4}{4 x + y})

将

y

视为常数

将常数提出:

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

= 4 \frac{\partial}{\partial x} (\frac{1}{4 x + y})

使用指数法则:

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

= 4 \frac{\partial}{\partial x} ((4 x + y)^{- 1})

使用连锁律:

- \frac{1}{( 4 x + y ) ^{2}} \frac{\partial}{\partial x} (4 x + y)

= - \frac{1}{( 4 x + y ) ^{2}} \frac{\partial}{\partial x} (4 x + y)

\frac{\partial}{\partial x} (4 x + y) = 4

= 4 (- \frac{1}{( 4 x + y ) ^{2}} \cdot 4)

化简

4 (- \frac{1}{( 4 x + y ) ^{2}} \cdot 4) : - \frac{16}{( 4 x + y ) ^{2}}

= - \frac{16}{( 4 x + y ) ^{2}}

n = 1 \sum \infty \frac{2 n}{3}

\frac{\partial}{\partial x} (3 e^{y})

\frac{\partial}{\partial x} (sin (2 x) cos (2 t))

\int \frac{ln ( 2 x )}{ln ( 4 x ) x} d x

\frac{d}{d x} ((x + 6)^{7} (x + 3)^{5})