derivative of 6^{6-x^2}

解

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

- ln (6) \cdot 3^{6 - x^{2}} \cdot 2^{- x^{2} + 7} x

解答ステップ

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

指数の規則を適用する:

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

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

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

連鎖法則を適用:

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

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

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

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

簡素化

e^{(6 - x^{2}) l n (6)} (- 2 ln (6) x) : - ln (6) \cdot 3^{6 - x^{2}} \cdot 2^{- x^{2} + 7} x

= - ln (6) \cdot 3^{6 - x^{2}} \cdot 2^{- x^{2} + 7} x