derivative 3^{sin(x)}

解

導関数

3^{s i n (x)}

ln (3) \cdot 3^{s i n (x)} cos (x)

解答ステップ

\frac{d}{d x} (3^{s i n (x)})

指数の規則を適用する:

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

3^{s i n (x)} = e^{s i n (x) l n (3)}

= \frac{d}{d x} (e^{s i n (x) l n (3)})

連鎖法則を適用:

e^{s i n (x) l n (3)} \frac{d}{d x} (sin (x) ln (3))

= e^{s i n (x) l n (3)} \frac{d}{d x} (sin (x) ln (3))

\frac{d}{d x} (sin (x) ln (3)) = ln (3) cos (x)

= e^{s i n (x) l n (3)} ln (3) cos (x)

e^{s i n (x) l n (3)} = 3^{s i n (x)}

= ln (3) \cdot 3^{s i n (x)} cos (x)