d/(dt)(((t^3)/4-2)+(4/t-3)+cos(t-2))

解

\frac{d}{d t} ((\frac{t ^{3}}{4} - 2) + (\frac{4}{t} - 3) + cos (t - 2))

\frac{3 t ^{2}}{4} - \frac{4}{t ^{2}} - sin (t - 2)

解答ステップ

\frac{d}{d t} ((\frac{t ^{3}}{4} - 2) + (\frac{4}{t} - 3) + cos (t - 2))

簡素化

(\frac{t ^{3}}{4} - 2) + (\frac{4}{t} - 3) + cos (t - 2) : \frac{t ^{3}}{4} + \frac{4}{t} + cos (t - 2) - 5

= \frac{d}{d t} (\frac{t ^{3}}{4} + \frac{4}{t} + cos (t - 2) - 5)

和/差の法則を適用:

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

= \frac{d}{d t} (\frac{t ^{3}}{4}) + \frac{d}{d t} (\frac{4}{t}) + \frac{d}{d t} (cos (t - 2)) - \frac{d}{d t} (5)

\frac{d}{d t} (\frac{t ^{3}}{4}) = \frac{3 t ^{2}}{4}

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

\frac{d}{d t} (cos (t - 2)) = - sin (t - 2)

\frac{d}{d t} (5) = 0

= \frac{3 t ^{2}}{4} - \frac{4}{t ^{2}} - sin (t - 2) - 0

簡素化

= \frac{3 t ^{2}}{4} - \frac{4}{t ^{2}} - sin (t - 2)