(\partial)/(\partial x)((xy)/(x+y)+z)

解答

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

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

求解步骤

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

将

y, z

视为常数

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (z) = 0

= \frac{y ^{2}}{( x + y ) ^{2}} + 0

化简

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

\frac{d}{d x} (\frac{( 2 x + 3 ) ^{4}}{( 3 x - 2 ) ^{5}})

\int_{a}^{b} arctan (x) d x

4 y^{^{'}} - (\frac{2}{x}) y = (- \frac{3}{2}) x y^{\frac{5}{2}}

x \to 0 lim (\frac{sin ( x )}{7 x})

\int \frac{5 x ^{4} + 7 x ^{2} + x + 2}{x ( x ^{2} + 1 ) ^{2}} d x