(\partial)/(\partial x)(-1/((10+x*y)))

解答

\frac{\partial}{\partial x} (- \frac{1}{( 10 + x \cdot y )})

\frac{y}{( 10 + x y ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (- \frac{1}{( 10 + x y )})

将

y

视为常数

将常数提出:

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

= - \frac{\partial}{\partial x} (\frac{1}{10 + x y})

使用指数法则:

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

= - \frac{\partial}{\partial x} ((10 + x y)^{- 1})

使用连锁律:

- \frac{1}{( 10 + x y ) ^{2}} \frac{\partial}{\partial x} (10 + x y)

= - \frac{1}{( 10 + x y ) ^{2}} \frac{\partial}{\partial x} (10 + x y)

\frac{\partial}{\partial x} (10 + x y) = y

= - (- \frac{1}{( 10 + x y ) ^{2}} y)

化简

- (- \frac{1}{( 10 + x y ) ^{2}} y) : \frac{y}{( 10 + x y ) ^{2}}

= \frac{y}{( 10 + x y ) ^{2}}

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

l a pl a ce t r an s f or m \frac{3}{2} sin (2 t)

x \to 3 lim (\frac{1}{x - 3})

f (x) = cos^{2} (2 - x^{2})

\int \frac{1}{a ^{2} + b ^{2} x ^{2}} d x