derivative f(x)= x/((x^2+15x+50))

解

導関数

f (x) = \frac{x}{( x ^{2} + 15 x + 50 )}

\frac{- x ^{2} + 50}{( x ^{2} + 15 x + 50 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x}{x ^{2} + 15 x + 50})

商の法則を適用:

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

= \frac{\frac{d x}{d x} ( x ^{2} + 15 x + 50 ) - \frac{d}{d x} ( x ^{2} + 15 x + 50 ) x}{( x ^{2} + 15 x + 50 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 15 x + 50) = 2 x + 15

= \frac{1 \cdot ( x ^{2} + 15 x + 50 ) - ( 2 x + 15 ) x}{( x ^{2} + 15 x + 50 ) ^{2}}

簡素化

\frac{1 \cdot ( x ^{2} + 15 x + 50 ) - ( 2 x + 15 ) x}{( x ^{2} + 15 x + 50 ) ^{2}} : \frac{- x ^{2} + 50}{( x ^{2} + 15 x + 50 ) ^{2}}

= \frac{- x ^{2} + 50}{( x ^{2} + 15 x + 50 ) ^{2}}