derivative of (sin(3x+1)/(7x^2+1))

解

\frac{d}{d x} (\frac{sin ( 3 x + 1 )}{7 x ^{2} + 1})

\frac{cos ( 3 x + 1 ) \cdot 3 ( 7 x ^{2} + 1 ) - 14 x sin ( 3 x + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{sin ( 3 x + 1 )}{7 x ^{2} + 1})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( sin ( 3 x + 1 ) ) ( 7 x ^{2} + 1 ) - \frac{d}{d x} ( 7 x ^{2} + 1 ) sin ( 3 x + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (sin (3 x + 1)) = cos (3 x + 1) \cdot 3

\frac{d}{d x} (7 x^{2} + 1) = 14 x

= \frac{cos ( 3 x + 1 ) \cdot 3 ( 7 x ^{2} + 1 ) - 14 x sin ( 3 x + 1 )}{( 7 x ^{2} + 1 ) ^{2}}