derivative 3^{x^2}

解

導関数

3^{x^{2}}

2 ln (3) \cdot 3^{x^{2}} x

解答ステップ

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

指数の規則を適用する:

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

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

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

連鎖法則を適用:

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

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

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

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

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

= 2 ln (3) \cdot 3^{x^{2}} x