d/(dt)(t^3-12t^2+45t)

解答

\frac{d}{d t} (t^{3} - 12 t^{2} + 45 t)

3 t^{2} - 24 t + 45

求解步骤

\frac{d}{d t} (t^{3} - 12 t^{2} + 45 t)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (t^{3}) - \frac{d}{d t} (12 t^{2}) + \frac{d}{d t} (45 t)

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

\frac{d}{d t} (12 t^{2}) = 24 t

\frac{d}{d t} (45 t) = 45

= 3 t^{2} - 24 t + 45

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