derivative of 3^{x-inx}

解

\frac{d}{d x} (3^{x - in x})

3^{x - in x} (ln (3) - i ln (3) n)

解答ステップ

\frac{d}{d x} (3^{x - in x})

指数の規則を適用する:

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

3^{x - in x} = e^{(x - in x) l n (3)}

= \frac{d}{d x} (e^{(x - in x) l n (3)})

連鎖法則を適用:

e^{(x - in x) l n (3)} \frac{d}{d x} ((x - in x) ln (3))

= e^{(x - in x) l n (3)} \frac{d}{d x} ((x - in x) ln (3))

\frac{d}{d x} ((x - in x) ln (3)) = ln (3) - i ln (3) n

= e^{(x - in x) l n (3)} (ln (3) - i ln (3) n)

e^{(x - in x) l n (3)} = 3^{x - in x}

= 3^{x - in x} (ln (3) - i ln (3) n)