derivative of 7^{x^2}

解

\frac{d}{d x} (7^{x^{2}})

2 ln (7) \cdot 7^{x^{2}} x

解答ステップ

\frac{d}{d x} (7^{x^{2}})

指数の規則を適用する:

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

7^{x^{2}} = e^{x^{2} l n (7)}

= \frac{d}{d x} (e^{x^{2} l n (7)})

連鎖法則を適用:

e^{x^{2} l n (7)} \frac{d}{d x} (x^{2} ln (7))

= e^{x^{2} l n (7)} \frac{d}{d x} (x^{2} ln (7))

\frac{d}{d x} (x^{2} ln (7)) = 2 ln (7) x

= e^{x^{2} l n (7)} \cdot 2 ln (7) x

e^{x^{2} l n (7)} = 7^{x^{2}}

= 2 ln (7) \cdot 7^{x^{2}} x