d/(dq)(500q-(q^2)/(ln(q+300)))

解

\frac{d}{d q} (500 q - \frac{q ^{2}}{ln ( q + 300 )})

500 - \frac{2 q ln ( q + 300 ) ( q + 300 ) - q ^{2}}{ln ^{2} ( q + 300 ) ( q + 300 )}

解答ステップ

\frac{d}{d q} (500 q - \frac{q ^{2}}{ln ( q + 300 )})

和/差の法則を適用:

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

= \frac{d}{d q} (500 q) - \frac{d}{d q} (\frac{q ^{2}}{ln ( q + 300 )})

\frac{d}{d q} (500 q) = 500

\frac{d}{d q} (\frac{q ^{2}}{ln ( q + 300 )}) = \frac{2 q ln ( q + 300 ) ( q + 300 ) - q ^{2}}{ln ^{2} ( q + 300 ) ( q + 300 )}

= 500 - \frac{2 q ln ( q + 300 ) ( q + 300 ) - q ^{2}}{ln ^{2} ( q + 300 ) ( q + 300 )}