derivative of ((6x^2+4)/((3y^2-4)))

解

\frac{d}{d x} (\frac{( 6 x ^{2} + 4 )}{( 3 y ^{2} - 4 )})

\frac{12 x ( 3 y ^{2} - 4 ) - 6 y \frac{d y}{d x} ( 6 x ^{2} + 4 )}{( 3 y ^{2} - 4 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{( 6 x ^{2} + 4 )}{( 3 y ^{2} - 4 )})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( 6 x ^{2} + 4 ) ( 3 y ^{2} - 4 ) - \frac{d}{d x} ( 3 y ^{2} - 4 ) ( 6 x ^{2} + 4 )}{( 3 y ^{2} - 4 ) ^{2}}

\frac{d}{d x} (6 x^{2} + 4) = 12 x

\frac{d}{d x} (3 y^{2} - 4) = 6 y \frac{d y}{d x}

= \frac{12 x ( 3 y ^{2} - 4 ) - 6 y \frac{d y}{d x} ( 6 x ^{2} + 4 )}{( 3 y ^{2} - 4 ) ^{2}}