derivative 4^{cosh(x)}

解

導関数

4^{c o s h (x)}

ln (2) \cdot 2^{2 c o s h (x) + 1} sinh (x)

解答ステップ

\frac{d}{d x} (4^{c o s h (x)})

指数の規則を適用する:

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

4^{c o s h (x)} = e^{c o s h (x) l n (4)}

= \frac{d}{d x} (e^{c o s h (x) l n (4)})

連鎖法則を適用:

e^{c o s h (x) l n (4)} \frac{d}{d x} (cosh (x) ln (4))

= e^{c o s h (x) l n (4)} \frac{d}{d x} (cosh (x) ln (4))

\frac{d}{d x} (cosh (x) ln (4)) = 2 ln (2) sinh (x)

= e^{c o s h (x) l n (4)} \cdot 2 ln (2) sinh (x)

簡素化

e^{c o s h (x) l n (4)} \cdot 2 ln (2) sinh (x) : ln (2) \cdot 2^{2 c o s h (x) + 1} sinh (x)

= ln (2) \cdot 2^{2 c o s h (x) + 1} sinh (x)