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

解答

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

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

求解步骤

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

将

y, z

视为常数

将常数提出:

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

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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

d er i v a t i v e f (x) = - 9 e^{x^{- 9}}

\frac{d}{d x} (- \frac{2}{1 - 2 x})

\frac{d}{d x} (\frac{1}{5 x})

x \to - 2 lim (3 x^{2} + 4 x - 2)

\frac{d y}{d x} = e^{4 x + 3 y}