derivative of tan(e^x*cosh(e^x))

解

\frac{d}{d x} (tan (e^{x}) \cdot cosh (e^{x}))

sec^{2} (e^{x}) e^{x} cosh (e^{x}) + sinh (e^{x}) e^{x} tan (e^{x})

解答ステップ

\frac{d}{d x} (tan (e^{x}) cosh (e^{x}))

積の法則を適用:

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

f = tan (e^{x}), g = cosh (e^{x})

= \frac{d}{d x} (tan (e^{x})) cosh (e^{x}) + \frac{d}{d x} (cosh (e^{x})) tan (e^{x})

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

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

= sec^{2} (e^{x}) e^{x} cosh (e^{x}) + sinh (e^{x}) e^{x} tan (e^{x})