derivative (9x)/(2^x)

解

導関数

\frac{9 x}{2 ^{x}}

\frac{9 ( 1 - ln ( 2 ) x )}{2 ^{x}}

解答ステップ

\frac{d}{d x} (\frac{9 x}{2 ^{x}})

定数を除去:

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

= 9 \frac{d}{d x} (\frac{x}{2 ^{x}})

商の法則を適用:

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

= 9 \cdot \frac{\frac{d x}{d x} 2 ^{x} - \frac{d}{d x} ( 2 ^{x} ) x}{( 2 ^{x} ) ^{2}}

\frac{d x}{d x} = 1

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

= 9 \cdot \frac{1 \cdot 2 ^{x} - 2 ^{x} ln ( 2 ) x}{( 2 ^{x} ) ^{2}}

簡素化

9 \cdot \frac{1 \cdot 2 ^{x} - 2 ^{x} ln ( 2 ) x}{( 2 ^{x} ) ^{2}} : \frac{9 ( 1 - ln ( 2 ) x )}{2 ^{x}}

= \frac{9 ( 1 - ln ( 2 ) x )}{2 ^{x}}