(\partial)/(\partial x)((93)/(2+x^2+y^2))

解答

\frac{\partial}{\partial x} (\frac{93}{2 + x ^{2} + y ^{2}})

- \frac{186 x}{( 2 + x ^{2} + y ^{2} ) ^{2}}

求解步骤

\frac{\partial}{\partial x} (\frac{93}{2 + x ^{2} + y ^{2}})

将

y

视为常数

将常数提出:

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

= 93 \frac{\partial}{\partial x} (\frac{1}{2 + x ^{2} + y ^{2}})

使用指数法则:

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

= 93 \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

= 93 (- \frac{1}{( 2 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x)

化简

93 (- \frac{1}{( 2 + x ^{2} + y ^{2} ) ^{2}} \cdot 2 x) : - \frac{186 x}{( 2 + x ^{2} + y ^{2} ) ^{2}}

= - \frac{186 x}{( 2 + x ^{2} + y ^{2} ) ^{2}}

x \to 1 lim (\frac{x}{∣ x ∣})

d er i v a t i v e y = (ln (x))^{l n (x)}

\frac{\partial}{\partial x} (\frac{z}{x + y})

\frac{d y}{d x} = \frac{( 2 x + 5 )}{( x ^{2} + 2 x )}, y (1) = 1

\int 2 x^{\frac{3}{2}} d x