d/(dt)((x)(4-8t^2))

解答

\frac{d}{d t} ((x) (4 - 8 t^{2}))

\frac{d x}{d t} (4 - 8 t^{2}) - 16 t x

求解步骤

\frac{d}{d t} ((x) (4 - 8 t^{2}))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 4 - 8 t^{2}

= \frac{d x}{d t} (4 - 8 t^{2}) + \frac{d}{d t} (4 - 8 t^{2}) x

\frac{d}{d t} (4 - 8 t^{2}) = - 16 t

= \frac{d x}{d t} (4 - 8 t^{2}) + (- 16 t) x

化简

= \frac{d x}{d t} (4 - 8 t^{2}) - 16 t x

e x p an d A (2, - 3) y B (8, 1)

e x p an d \frac{( x ^{2} + 4 ) 9 - x ^{2}}{x ^{3} - 1}

e x p an d x (x d v + v d x)

e x p an d n o t a v e i s (- 5 + \frac{x ^{2}}{2})^{3}

e x p an d \frac{1}{( 1 + e ^{- x} ) ^{2}}