derivative of x/(3-{z(x)})

解

\frac{d}{d x} (\frac{x}{3 - z ( x )})

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

解答ステップ

\frac{d}{d x} (\frac{x}{3 - z ( x )})

商の法則を適用:

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

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

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

\frac{d}{d x} (3 - z (x)) = - \frac{d}{d x} (z (x))

= \frac{1 \cdot ( 3 - z ( x ) ) - ( - \frac{d}{d x} ( z ( x ) ) ) x}{( 3 - z ( x ) ) ^{2}}

簡素化

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