derivative of x/(x+20)

解答

\frac{d}{d x} (\frac{x}{x + 20})

\frac{20}{( x + 20 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x}{x + 20})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} ( x + 20 ) - \frac{d}{d x} ( x + 20 ) x}{( x + 20 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (x + 20) = 1

= \frac{1 \cdot ( x + 20 ) - 1 \cdot x}{( x + 20 ) ^{2}}

1 \cdot (x + 20) - 1 \cdot x = 20

= \frac{20}{( x + 20 ) ^{2}}

\int \frac{2 x}{x + 2} d x

\frac{d y}{d x} = 0.0225 y + 0.0003 y^{2}

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

\frac{\partial}{\partial x} (x^{2} y + 3 x y + y^{2})

x \to \infty lim ((\frac{( 2 x - 3 )}{( 2 x + 5 )})^{2 x + 1})