derivative of re^{rx}

解

\frac{d}{d x} (r (x) e^{r (x) x})

\frac{d r}{d x} e^{r x} + e^{r x} (x \frac{d r}{d x} + r) r

解答ステップ

\frac{d}{d x} (r e^{r x})

積の法則を適用:

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

f = r, g = e^{r x}

= \frac{d r}{d x} e^{r x} + \frac{d}{d x} (e^{r x}) r

\frac{d}{d x} (e^{r x}) = e^{r x} (x \frac{d r}{d x} + r)

= \frac{d r}{d x} e^{r x} + e^{r x} (x \frac{d r}{d x} + r) r