d/(dy)((x)(e^x+x^e))

解

\frac{d}{d y} ((y) (e^{y} + y^{e}))

e^{y} + y^{e} + y (e^{y} + e y^{e - 1})

解答ステップ

\frac{d}{d y} ((y) (e^{y} + y^{e}))

積の法則を適用:

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

f = y, g = e^{y} + y^{e}

= \frac{d y}{d y} (e^{y} + y^{e}) + \frac{d}{d y} (e^{y} + y^{e}) y

\frac{d y}{d y} = 1

\frac{d}{d y} (e^{y} + y^{e}) = e^{y} + e y^{e - 1}

= 1 \cdot (e^{y} + y^{e}) + (e^{y} + e y^{e - 1}) y

簡素化

= e^{y} + y^{e} + y (e^{y} + e y^{e - 1})