derivative of cosh(xsinh(x))

解

\frac{d}{d x} (cosh (x) sinh (x))

sinh^{2} (x) + cosh^{2} (x)

解答ステップ

\frac{d}{d x} (cosh (x) sinh (x))

積の法則を適用:

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

f = cosh (x), g = sinh (x)

= \frac{d}{d x} (cosh (x)) sinh (x) + \frac{d}{d x} (sinh (x)) cosh (x)

\frac{d}{d x} (cosh (x)) = sinh (x)

\frac{d}{d x} (sinh (x)) = cosh (x)

= sinh (x) sinh (x) + cosh (x) cosh (x)

簡素化

sinh (x) sinh (x) + cosh (x) cosh (x) : sinh^{2} (x) + cosh^{2} (x)

= sinh^{2} (x) + cosh^{2} (x)