derivative of 2^xtan(3x)

解

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

2^{x} ln (2) tan (3 x) + sec^{2} (3 x) \cdot 3 \cdot 2^{x}

解答ステップ

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

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2^{x}, g = tan (3 x)

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

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

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

= 2^{x} ln (2) tan (3 x) + sec^{2} (3 x) \cdot 3 \cdot 2^{x}