derivative of (2e^x-4x-6/(5sin(x)-3))

解

\frac{d}{d x} (\frac{2 e ^{x} - 4 x - 6}{5 sin ( x ) - 3})

\frac{( 2 e ^{x} - 4 ) ( 5 sin ( x ) - 3 ) - 5 cos ( x ) ( 2 e ^{x} - 4 x - 6 )}{( 5 sin ( x ) - 3 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{2 e ^{x} - 4 x - 6}{5 sin ( x ) - 3})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( 2 e ^{x} - 4 x - 6 ) ( 5 sin ( x ) - 3 ) - \frac{d}{d x} ( 5 sin ( x ) - 3 ) ( 2 e ^{x} - 4 x - 6 )}{( 5 sin ( x ) - 3 ) ^{2}}

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

\frac{d}{d x} (5 sin (x) - 3) = 5 cos (x)

= \frac{( 2 e ^{x} - 4 ) ( 5 sin ( x ) - 3 ) - 5 cos ( x ) ( 2 e ^{x} - 4 x - 6 )}{( 5 sin ( x ) - 3 ) ^{2}}