derivative 3t^3-2/(t^2)

解答

导数

3 t^{3} - \frac{2}{t ^{2}}

9 t^{2} + \frac{4}{t ^{3}}

求解步骤

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

使用微分加减法定则:

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

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

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

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

= 9 t^{2} - (- \frac{4}{t ^{3}})

化简

= 9 t^{2} + \frac{4}{t ^{3}}