d/(dt)(2^{t^3})

解

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

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

解答ステップ

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

指数の規則を適用する:

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

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

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

連鎖法則を適用:

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

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

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

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

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

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