derivative 4^{(x^9)}

解

導関数

4^{(x^{9})}

9 ln (2) \cdot 2^{2 x^{9} + 1} x^{8}

解答ステップ

\frac{d}{d x} (4^{x^{9}})

指数の規則を適用する:

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

4^{x^{9}} = e^{x^{9} l n (4)}

= \frac{d}{d x} (e^{x^{9} l n (4)})

連鎖法則を適用:

e^{x^{9} l n (4)} \frac{d}{d x} (x^{9} ln (4))

= e^{x^{9} l n (4)} \frac{d}{d x} (x^{9} ln (4))

\frac{d}{d x} (x^{9} ln (4)) = 18 ln (2) x^{8}

= e^{x^{9} l n (4)} \cdot 18 ln (2) x^{8}

簡素化

e^{x^{9} l n (4)} \cdot 18 ln (2) x^{8} : 9 ln (2) \cdot 2^{2 x^{9} + 1} x^{8}

= 9 ln (2) \cdot 2^{2 x^{9} + 1} x^{8}