(\partial)/(\partial x)(y^{x^7})

解

\frac{\partial}{\partial x} (y^{x^{7}})

7 x^{6} y^{x^{7}} ln (y)

解答ステップ

\frac{\partial}{\partial x} (y^{x^{7}})

y

を定数として扱う

指数の規則を適用する:

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

y^{x^{7}} = e^{x^{7} l n (y)}

= \frac{\partial}{\partial x} (e^{x^{7} l n (y)})

連鎖法則を適用:

e^{x^{7} l n (y)} \frac{\partial}{\partial x} (x^{7} ln (y))

= e^{x^{7} l n (y)} \frac{\partial}{\partial x} (x^{7} ln (y))

\frac{\partial}{\partial x} (x^{7} ln (y)) = 7 x^{6} ln (y)

= e^{x^{7} l n (y)} \cdot 7 x^{6} ln (y)

e^{x^{7} l n (y)} = y^{x^{7}}

= 7 x^{6} y^{x^{7}} ln (y)