(\partial)/(\partial x)((63)/((9+x^2+y^2)))

解答

\frac{\partial}{\partial x} (\frac{63}{( 9 + x ^{2} + y ^{2} )})

- \frac{126 x}{( 9 + x ^{2} + y ^{2} ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{63}{( 9 + x ^{2} + y ^{2} )})

将

y

视为常数

将常数提出:

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

= 63 \frac{\partial}{\partial x} (\frac{1}{9 + x ^{2} + y ^{2}})

使用指数法则:

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

= 63 \frac{\partial}{\partial x} ((9 + x^{2} + y^{2})^{- 1})

使用连锁律:

- \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (9 + x^{2} + y^{2})

= - \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \frac{\partial}{\partial x} (9 + x^{2} + y^{2})

\frac{\partial}{\partial x} (9 + x^{2} + y^{2}) = 2 x

= 63 (- \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

化简

63 (- \frac{1}{( 9 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{126 x}{( 9 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{126 x}{( 9 + x ^{2} + y ^{2} ) ^{2}}

\int \frac{d y}{y} d x

(e^{c o s (x)})^{^{'}}

\int (3 x - 8)^{21} d x

n = 4 \sum \infty \frac{3 ^{n}}{1 0 ^{n}}

\int 5 x^{2} d x