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

Lösung

\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})

Schritte zur Lösung

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

Wende die Produktregel an:

(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})

\frac{d ^{4}}{d x ^{4}} (ln (x + 1))

\frac{d y}{d x} = (x + 1)

y^{^{''''}} + 2 \cdot y^{^{''}} + y = 0

\frac{\partial}{\partial y} (2 x y + 2 x)

\frac{d}{d x} (sin^{2} (8 x))