derivative of x/(1+(1.5574+5.43x^2^2))

解

\frac{d}{d x} (\frac{x}{1 + ( 1.5574 + 5.43 x ^{2} ) ^{2}})

\frac{- 88.4547 x ^{4} - 16.913364 x ^{2} + 3.42549476}{( 29.4849 x ^{4} + 16.913364 x ^{2} + 3.42549476 ) ^{2}}

解答ステップ

\frac{d}{d x} (\frac{x}{1 + ( 1.5574 + 5.43 x ^{2} ) ^{2}})

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} ( 1 + ( 1.5574 + 5.43 x ^{2} ) ^{2} ) - \frac{d}{d x} ( 1 + ( 1.5574 + 5.43 x ^{2} ) ^{2} ) x}{( 1 + ( 1.5574 + 5.43 x ^{2} ) ^{2} ) ^{2}}

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

\frac{d}{d x} (1 + (1.5574 + 5.43 x^{2})^{2}) = 21.72 x (5.43 x^{2} + 1.5574)

= \frac{1 \cdot ( 1 + ( 1.5574 + 5.43 x ^{2} ) ^{2} ) - 21.72 x ( 5.43 x ^{2} + 1.5574 ) x}{( 1 + ( 1.5574 + 5.43 x ^{2} ) ^{2} ) ^{2}}

簡素化

\frac{1 \cdot ( 1 + ( 1.5574 + 5.43 x ^{2} ) ^{2} ) - 21.72 x ( 5.43 x ^{2} + 1.5574 ) x}{( 1 + ( 1.5574 + 5.43 x ^{2} ) ^{2} ) ^{2}} : \frac{- 88.4547 x ^{4} - 16.913364 x ^{2} + 3.42549476}{( 29.4849 x ^{4} + 16.913364 x ^{2} + 3.42549476 ) ^{2}}

= \frac{- 88.4547 x ^{4} - 16.913364 x ^{2} + 3.42549476}{( 29.4849 x ^{4} + 16.913364 x ^{2} + 3.42549476 ) ^{2}}