derivative of a^{6x^2}

解

\frac{d}{d x} (a^{6 x^{2}})

12 a^{6 x^{2}} x ln (a)

解答ステップ

\frac{d}{d x} (a^{6 x^{2}})

指数の規則を適用する:

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

a^{6 x^{2}} = e^{6 x^{2} l n (a)}

= \frac{d}{d x} (e^{6 x^{2} l n (a)})

連鎖法則を適用:

e^{6 x^{2} l n (a)} \frac{d}{d x} (6 x^{2} ln (a))

= e^{6 x^{2} l n (a)} \frac{d}{d x} (6 x^{2} ln (a))

\frac{d}{d x} (6 x^{2} ln (a)) = 12 x ln (a)

= e^{6 x^{2} l n (a)} \cdot 12 x ln (a)

e^{6 x^{2} l n (a)} = a^{6 x^{2}}

= 12 a^{6 x^{2}} x ln (a)