derivative 0.49489nv^2+1500*n/v

解

導関数

0.49489 n v^{2} + 1500 \cdot \frac{n}{v}

0.98978 n v - \frac{1500 n}{v ^{2}}

解答ステップ

\frac{d}{d v} (0.49489 n v^{2} + 1500 \cdot \frac{n}{v})

簡素化

0.49489 n v^{2} + 1500 \cdot \frac{n}{v} : 0.49489 n v^{2} + \frac{1500 n}{v}

= \frac{d}{d v} (0.49489 n v^{2} + \frac{1500 n}{v})

和/差の法則を適用:

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

= \frac{d}{d v} (0.49489 n v^{2}) + \frac{d}{d v} (\frac{1500 n}{v})

\frac{d}{d v} (0.49489 n v^{2}) = 0.98978 n v

\frac{d}{d v} (\frac{1500 n}{v}) = - \frac{1500 n}{v ^{2}}

= 0.98978 n v - \frac{1500 n}{v ^{2}}