d/(dt)((x)(3x^3-30))

解答

\frac{d}{d t} ((t) (3 t^{3} - 30))

12 t^{3} - 30

求解步骤

\frac{d}{d t} ((t) (3 t^{3} - 30))

使用微分乘法定则:

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

f = t, g = 3 t^{3} - 30

= \frac{d t}{d t} (3 t^{3} - 30) + \frac{d}{d t} (3 t^{3} - 30) t

\frac{d t}{d t} = 1

\frac{d}{d t} (3 t^{3} - 30) = 9 t^{2}

= 1 \cdot (3 t^{3} - 30) + 9 t^{2} t

化简

1 \cdot (3 t^{3} - 30) + 9 t^{2} t : 12 t^{3} - 30

= 12 t^{3} - 30

e x p an d 7 (x - 1 = 3 x - 1)

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