(\partial)/(\partial x)(2y^{4x})

解

\frac{\partial}{\partial x} (2 y^{4 x})

8 y^{4 x} ln (y)

解答ステップ

\frac{\partial}{\partial x} (2 y^{4 x})

y

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{\partial}{\partial x} (y^{4 x})

指数の規則を適用する:

a^{b} = e^{b l n (a)}

y^{4 x} = e^{4 x l n (y)}

= 2 \frac{\partial}{\partial x} (e^{4 x l n (y)})

連鎖法則を適用:

e^{4 x l n (y)} \frac{\partial}{\partial x} (4 x ln (y))

= e^{4 x l n (y)} \frac{\partial}{\partial x} (4 x ln (y))

\frac{\partial}{\partial x} (4 x ln (y)) = 4 ln (y)

= 2 e^{4 x l n (y)} \cdot 4 ln (y)

簡素化

2 e^{4 x l n (y)} \cdot 4 ln (y) : 8 y^{4 x} ln (y)

= 8 y^{4 x} ln (y)