d/(dr(t))((t)(t^{r(t)}))

解

\frac{d ^{2}}{d r d t} ((t) (t^{r (t)}))

t^{t r + 2} ln (t) (r ln (t) + \frac{t r + 2}{t}) + t^{t r + 1}

解答ステップ

\frac{d ^{2}}{d r d t} ((t) (t^{r (t)}))

\frac{d}{d r} (t t^{r t}) = t^{t r + 2} ln (t)

= \frac{d}{d t} (t^{t r + 2} ln (t))

\frac{d}{d t} (t^{t r + 2} ln (t)) = t^{t r + 2} ln (t) (r ln (t) + \frac{t r + 2}{t}) + t^{t r + 1}

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