d/(d{r)}({r}sqrt(1-{r)^2})

解

\frac{d}{d r} (r 1 - r^{2})

1 - r^{2} - \frac{r ^{2}}{1 - r ^{2}}

解答ステップ

\frac{d}{d r} (r 1 - r^{2})

積の法則を適用:

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

f = r, g = 1 - r^{2}

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

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

\frac{d}{d r} (1 - r^{2}) = - \frac{r}{1 - r ^{2}}

= 1 \cdot 1 - r^{2} + (- \frac{r}{1 - r ^{2}}) r

簡素化

1 \cdot 1 - r^{2} + (- \frac{r}{1 - r ^{2}}) r : 1 - r^{2} - \frac{r ^{2}}{1 - r ^{2}}

= 1 - r^{2} - \frac{r ^{2}}{1 - r ^{2}}