derivative of 3^{tan(x})

解

\frac{d}{d x} (3^{t a n (x)})

ln (3) \cdot 3^{t a n (x)} sec^{2} (x)

解答ステップ

\frac{d}{d x} (3^{t a n (x)})

指数の規則を適用する:

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

3^{t a n (x)} = e^{t a n (x) l n (3)}

= \frac{d}{d x} (e^{t a n (x) l n (3)})

連鎖法則を適用:

e^{t a n (x) l n (3)} \frac{d}{d x} (tan (x) ln (3))

= e^{t a n (x) l n (3)} \frac{d}{d x} (tan (x) ln (3))

\frac{d}{d x} (tan (x) ln (3)) = ln (3) sec^{2} (x)

= e^{t a n (x) l n (3)} ln (3) sec^{2} (x)

e^{t a n (x) l n (3)} = 3^{t a n (x)}

= ln (3) \cdot 3^{t a n (x)} sec^{2} (x)