derivative of 500(1+(4x/(50+x^2)))

解

\frac{d}{d x} (500 (1 + \frac{4 x}{50 + x ^{2}}))

\frac{2000 ( - x ^{2} + 50 )}{( x ^{2} + 50 ) ^{2}}

解答ステップ

\frac{d}{d x} (500 (1 + \frac{4 x}{50 + x ^{2}}))

定数を除去:

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

= 500 \frac{d}{d x} (1 + \frac{4 x}{50 + x ^{2}})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 500 (\frac{d}{d x} (1) + \frac{d}{d x} (\frac{4 x}{50 + x ^{2}}))

\frac{d}{d x} (1) = 0

\frac{d}{d x} (\frac{4 x}{50 + x ^{2}}) = \frac{4 ( 50 - x ^{2} )}{( 50 + x ^{2} ) ^{2}}

= 500 (0 + \frac{4 ( 50 - x ^{2} )}{( 50 + x ^{2} ) ^{2}})

簡素化

500 (0 + \frac{4 ( 50 - x ^{2} )}{( 50 + x ^{2} ) ^{2}}) : \frac{2000 ( - x ^{2} + 50 )}{( x ^{2} + 50 ) ^{2}}

= \frac{2000 ( - x ^{2} + 50 )}{( x ^{2} + 50 ) ^{2}}