derivative of (2^x/(cos(x)))

解

\frac{d}{d x} (\frac{2 ^{x}}{cos ( x )})

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

解答ステップ

\frac{d}{d x} (\frac{2 ^{x}}{cos ( x )})

簡素化

\frac{2 ^{x}}{cos ( x )} : 2^{x} sec (x)

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

積の法則を適用:

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

f = 2^{x}, g = sec (x)

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

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

\frac{d}{d x} (sec (x)) = sec (x) tan (x)

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