derivative of 8^{4-x^2}

解

\frac{d}{d x} (8^{4 - x^{2}})

- 3 ln (2) \cdot 2^{- 3 x^{2} + 13} x

解答ステップ

\frac{d}{d x} (8^{4 - x^{2}})

指数の規則を適用する:

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

8^{4 - x^{2}} = e^{(4 - x^{2}) l n (8)}

= \frac{d}{d x} (e^{(4 - x^{2}) l n (8)})

連鎖法則を適用:

e^{(4 - x^{2}) l n (8)} \frac{d}{d x} ((4 - x^{2}) ln (8))

= e^{(4 - x^{2}) l n (8)} \frac{d}{d x} ((4 - x^{2}) ln (8))

\frac{d}{d x} ((4 - x^{2}) ln (8)) = - 6 ln (2) x

= e^{(4 - x^{2}) l n (8)} (- 6 ln (2) x)

簡素化

e^{(4 - x^{2}) l n (8)} (- 6 ln (2) x) : - 3 ln (2) \cdot 2^{- 3 x^{2} + 13} x

= - 3 ln (2) \cdot 2^{- 3 x^{2} + 13} x