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

解答

\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}}

求解步骤

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

使用微分除法定则:

(\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}}

化简

\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}}

\int x^{5} e^{- 3 x} d x

n = 1 \sum \infty \frac{n !}{10 2 ^{n}}

f (x) = - \frac{x ^{3} + x - 1}{2}

d er i v a t i v e y = \frac{9}{8 4 x ^{3}}

x \to 0 lim (a^{x})