derivative of (x^2/(1+2tan(x)))

解

\frac{d}{d x} (\frac{x ^{2}}{1 + 2 tan ( x )})

\frac{2 x ( 1 + 2 tan ( x ) ) - 2 sec ^{2} ( x ) x ^{2}}{( 1 + 2 tan ( x ) ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x ^{2}}{1 + 2 tan ( x )})

商の法則を適用:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( 1 + 2 tan ( x ) ) - \frac{d}{d x} ( 1 + 2 tan ( x ) ) x ^{2}}{( 1 + 2 tan ( x ) ) ^{2}}

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

\frac{d}{d x} (1 + 2 tan (x)) = 2 sec^{2} (x)

= \frac{2 x ( 1 + 2 tan ( x ) ) - 2 sec ^{2} ( x ) x ^{2}}{( 1 + 2 tan ( x ) ) ^{2}}