(\partial)/(\partial r)(rln(rs^2t^3))

解

\frac{\partial}{\partial r} (r ln (r s^{2} t^{3}))

ln (r s^{2} t^{3}) + 1

解答ステップ

\frac{\partial}{\partial r} (r ln (r s^{2} t^{3}))

s, t

を定数として扱う

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = r, g = ln (r s^{2} t^{3})

= \frac{\partial}{\partial r} (r) ln (r s^{2} t^{3}) + \frac{\partial}{\partial r} (ln (r s^{2} t^{3})) r

\frac{\partial}{\partial r} (r) = 1

\frac{\partial}{\partial r} (ln (r s^{2} t^{3})) = \frac{1}{r}

= 1 \cdot ln (r s^{2} t^{3}) + \frac{1}{r} r

簡素化

1 \cdot ln (r s^{2} t^{3}) + \frac{1}{r} r : ln (r s^{2} t^{3}) + 1

= ln (r s^{2} t^{3}) + 1