d/(dt)(at-tanh(at))

Lösung

\frac{d}{d t} (a t - tanh (a t))

a tanh^{2} (a t)

Schritte zur Lösung

\frac{d}{d t} (a t - tanh (a t))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (a t) - \frac{d}{d t} (tanh (a t))

\frac{d}{d t} (a t) = a

\frac{d}{d t} (tanh (a t)) = sech^{2} (a t) a

= a - sech^{2} (a t) a

Vereinfache

a - sech^{2} (a t) a : a tanh^{2} (a t)

= a tanh^{2} (a t)