derivative of (3y^2/(x^2-4))

解

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

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

解答ステップ

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

定数を除去:

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

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

商の法則を適用:

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

= 3 \cdot \frac{\frac{d}{d x} ( y ^{2} ) ( x ^{2} - 4 ) - \frac{d}{d x} ( x ^{2} - 4 ) y ^{2}}{( x ^{2} - 4 ) ^{2}}

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

\frac{d}{d x} (x^{2} - 4) = 2 x

= 3 \cdot \frac{2 y \frac{d y}{d x} ( x ^{2} - 4 ) - 2 x y ^{2}}{( x ^{2} - 4 ) ^{2}}

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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