derivative of 2^{(x^2+1})

解

\frac{d}{d x} (2^{(x^{2} + 1)})

ln (2) \cdot 2^{x^{2} + 2} x

解答ステップ

\frac{d}{d x} (2^{(x^{2} + 1)})

指数の規則を適用する:

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

2^{x^{2} + 1} = e^{(x^{2} + 1) l n (2)}

= \frac{d}{d x} (e^{(x^{2} + 1) l n (2)})

連鎖法則を適用:

e^{(x^{2} + 1) l n (2)} \frac{d}{d x} ((x^{2} + 1) ln (2))

= e^{(x^{2} + 1) l n (2)} \frac{d}{d x} ((x^{2} + 1) ln (2))

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

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

簡素化

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

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