d/(dt)((x)(2t+2t^3))

解答

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

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

求解步骤

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

使用微分乘法定则:

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

f = x, g = 2 t + 2 t^{3}

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

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

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

e x p an d A (4, - 10) B (- 6, - 8)

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