(\partial)/(\partial x)((26)/((2+x^2+y^2)))

解答

\frac{\partial}{\partial x} (\frac{26}{( 2 + x ^{2} + y ^{2} )})

- \frac{52 x}{( 2 + x ^{2} + y ^{2} ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{26}{( 2 + x ^{2} + y ^{2} )})

将

y

视为常数

将常数提出:

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

= 26 \frac{\partial}{\partial x} (\frac{1}{2 + x ^{2} + y ^{2}})

使用指数法则:

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

= 26 \frac{\partial}{\partial x} ((2 + x^{2} + y^{2})^{- 1})

使用连锁律:

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

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

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

= 26 (- \frac{1}{( 2 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

化简

26 (- \frac{1}{( 2 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{52 x}{( 2 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{52 x}{( 2 + x ^{2} + y ^{2} ) ^{2}}

\int e^{x} \cdot 7 x d x

(u^{2} + u) d x + u^{2} (x d u + u d x) = 0

x \to 4 lim (e^{x} + 4 x)

\int 3 2 x d x

\frac{\partial}{\partial x} (7 x sin (5 x^{2} y))