derivative of (5x^2/(x+47))

解

\frac{d}{d x} (\frac{5 x ^{2}}{x + 47})

\frac{5 ( x ^{2} + 94 x )}{( x + 47 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{5 x ^{2}}{x + 47})

定数を除去:

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

= 5 \frac{d}{d x} (\frac{x ^{2}}{x + 47})

商の法則を適用:

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

= 5 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( x + 47 ) - \frac{d}{d x} ( x + 47 ) x ^{2}}{( x + 47 ) ^{2}}

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

\frac{d}{d x} (x + 47) = 1

= 5 \cdot \frac{2 x ( x + 47 ) - 1 \cdot x ^{2}}{( x + 47 ) ^{2}}

簡素化

5 \cdot \frac{2 x ( x + 47 ) - 1 \cdot x ^{2}}{( x + 47 ) ^{2}} : \frac{5 ( x ^{2} + 94 x )}{( x + 47 ) ^{2}}

= \frac{5 ( x ^{2} + 94 x )}{( x + 47 ) ^{2}}