(\partial)/(\partial x)(3/(3x+5y))

解答

\frac{\partial}{\partial x} (\frac{3}{3 x + 5 y})

- \frac{9}{( 3 x + 5 y ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{3}{3 x + 5 y})

将

y

视为常数

将常数提出:

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

= 3 \frac{\partial}{\partial x} (\frac{1}{3 x + 5 y})

使用指数法则:

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

= 3 \frac{\partial}{\partial x} ((3 x + 5 y)^{- 1})

使用连锁律:

- \frac{1}{( 3 x + 5 y ) ^{2}} \frac{\partial}{\partial x} (3 x + 5 y)

= - \frac{1}{( 3 x + 5 y ) ^{2}} \frac{\partial}{\partial x} (3 x + 5 y)

\frac{\partial}{\partial x} (3 x + 5 y) = 3

= 3 (- \frac{1}{( 3 x + 5 y ) ^{2}} \cdot 3)

化简

3 (- \frac{1}{( 3 x + 5 y ) ^{2}} \cdot 3) : - \frac{9}{( 3 x + 5 y ) ^{2}}

= - \frac{9}{( 3 x + 5 y ) ^{2}}

a re a 6 x^{2} ln (x), 24 ln (x)

\frac{d y}{d x} = \frac{1}{2} x + 2

x^{2} y^{^{''}} + 3 x y^{^{'}} + 2 y = 0, y (1) = 0.2, y^{^{'}} (1) = 0.3

\frac{d}{d x} (cos (sin (tan (π) x)))

l a pl a ce t r an s f or m 3 \cdot sin (3 t + 2)