(\partial)/(\partial x)(((9y+7z))/(x+u))

解答

\frac{\partial}{\partial x} (\frac{( 9 y + 7 z )}{x + u})

- \frac{9 y + 7 z}{( x + u ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{( 9 y + 7 z )}{x + u})

将

y, z, u

视为常数

将常数提出:

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

= (9 y + 7 z) \frac{\partial}{\partial x} (\frac{1}{x + u})

使用指数法则:

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

= (9 y + 7 z) \frac{\partial}{\partial x} ((x + u)^{- 1})

使用连锁律:

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

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

\frac{\partial}{\partial x} (x + u) = 1

= (9 y + 7 z) (- \frac{1}{( x + u ) ^{2}} \cdot 1)

化简

(9 y + 7 z) (- \frac{1}{( x + u ) ^{2}} \cdot 1) : - \frac{9 y + 7 z}{( x + u ) ^{2}}

= - \frac{9 y + 7 z}{( x + u ) ^{2}}

\int \frac{3 r ^{2}}{r + 5} d r

s l o p e in t erce pt (3, 5), (1, - 7)

x \to 0 lim (\frac{( 2 + x ^{3} ) - 8}{x})

\int_{0}^{2} \frac{5 t}{( t - 3 ) ^{2}} d t

\frac{d}{d x} (ln (- 5 x))