d/(dt)((x)(6t^2-t^3))

解答

\frac{d}{d t} ((x) (6 t^{2} - t^{3}))

\frac{d x}{d t} (6 t^{2} - t^{3}) + (12 t - 3 t^{2}) x

求解步骤

\frac{d}{d t} ((x) (6 t^{2} - t^{3}))

使用微分乘法定则:

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

f = x, g = 6 t^{2} - t^{3}

= \frac{d x}{d t} (6 t^{2} - t^{3}) + \frac{d}{d t} (6 t^{2} - t^{3}) x

\frac{d}{d t} (6 t^{2} - t^{3}) = 12 t - 3 t^{2}

= \frac{d x}{d t} (6 t^{2} - t^{3}) + (12 t - 3 t^{2}) x

\frac{d}{d x} ((y^{3}) c (x - c)^{2})

e x p an d (x^{2} - 2 x - 3)^{5}

e x p an d (8 x - 20) \circ

e x p an d \frac{4 x}{( 79 - x ) ( 21 - x )}

e x p an d 20 x^{21} x^{22} x^{23}