derivative 10+(50x)/(2x^2+9)

解

導関数

10 + \frac{50 x}{2 x ^{2} + 9}

\frac{50 ( - 2 x ^{2} + 9 )}{( 2 x ^{2} + 9 ) ^{2}}

解答ステップ

\frac{d}{d x} (10 + \frac{50 x}{2 x ^{2} + 9})

和/差の法則を適用:

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

= \frac{d}{d x} (10) + \frac{d}{d x} (\frac{50 x}{2 x ^{2} + 9})

\frac{d}{d x} (10) = 0

\frac{d}{d x} (\frac{50 x}{2 x ^{2} + 9}) = \frac{50 ( - 2 x ^{2} + 9 )}{( 2 x ^{2} + 9 ) ^{2}}

= 0 + \frac{50 ( - 2 x ^{2} + 9 )}{( 2 x ^{2} + 9 ) ^{2}}

簡素化

= \frac{50 ( - 2 x ^{2} + 9 )}{( 2 x ^{2} + 9 ) ^{2}}