derivative 6^{2^{x^2}}

解

導関数

6^{2^{x^{2}}}

ln (6) ln (2) \cdot 3^{2^{x^{2}}} \cdot 2^{2^{x^{2}} + x^{2} + 1} x

解答ステップ

\frac{d}{d x} (6^{2^{x^{2}}})

指数の規則を適用する:

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

6^{2^{x^{2}}} = e^{2^{x^{2}} l n (6)}

= \frac{d}{d x} (e^{2^{x^{2}} l n (6)})

連鎖法則を適用:

e^{2^{x^{2}} l n (6)} \frac{d}{d x} (2^{x^{2}} ln (6))

= e^{2^{x^{2}} l n (6)} \frac{d}{d x} (2^{x^{2}} ln (6))

\frac{d}{d x} (2^{x^{2}} ln (6)) = ln (6) ln (2) \cdot 2^{x^{2} + 1} x

= e^{2^{x^{2}} l n (6)} ln (6) ln (2) \cdot 2^{x^{2} + 1} x

簡素化

e^{2^{x^{2}} l n (6)} ln (6) ln (2) \cdot 2^{x^{2} + 1} x : ln (6) ln (2) \cdot 3^{2^{x^{2}}} \cdot 2^{2^{x^{2}} + x^{2} + 1} x

= ln (6) ln (2) \cdot 3^{2^{x^{2}}} \cdot 2^{2^{x^{2}} + x^{2} + 1} x