(\partial)/(\partial t)(sech^2(x-t))

Lösung

\frac{\partial}{\partial t} (sech^{2} (x - t))

2 sech^{2} (x - t) tanh (x - t)

Schritte zur Lösung

\frac{\partial}{\partial t} (sech^{2} (x - t))

Behandle

x

als Konstante

Wende die Kettenregel an:

2 sech (x - t) \frac{\partial}{\partial t} (sech (x - t))

= 2 sech (x - t) \frac{\partial}{\partial t} (sech (x - t))

\frac{\partial}{\partial t} (sech (x - t)) = sech (x - t) tanh (x - t)

= 2 sech (x - t) sech (x - t) tanh (x - t)

Vereinfache

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

= 2 sech^{2} (x - t) tanh (x - t)

\int 6 x^{4} e^{x^{5}} d x

\frac{d}{d x} ((2 x^{2} - 2 x) l e f (x, t) t (x^{2} - 3))

d er i v a t i v e f (x) = (2 + 5 x)^{2}

x \to 0 + lim (\frac{1}{x} - \frac{1}{x ^{2} + x})

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