derivative f(x)=2^{x^3}

解

導関数

f (x) = 2^{x^{3}}

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

解答ステップ

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

指数の規則を適用する:

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

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

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

連鎖法則を適用:

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

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

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

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

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

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