derivative of a^{3x^2}

解

\frac{d}{d x} (a^{3 x^{2}})

6 a^{3 x^{2}} x ln (a)

解答ステップ

\frac{d}{d x} (a^{3 x^{2}})

指数の規則を適用する:

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

a^{3 x^{2}} = e^{3 x^{2} l n (a)}

= \frac{d}{d x} (e^{3 x^{2} l n (a)})

連鎖法則を適用:

e^{3 x^{2} l n (a)} \frac{d}{d x} (3 x^{2} ln (a))

= e^{3 x^{2} l n (a)} \frac{d}{d x} (3 x^{2} ln (a))

\frac{d}{d x} (3 x^{2} ln (a)) = 6 x ln (a)

= e^{3 x^{2} l n (a)} \cdot 6 x ln (a)

e^{3 x^{2} l n (a)} = a^{3 x^{2}}

= 6 a^{3 x^{2}} x ln (a)