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

Lösung

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

- 2 x t

Schritte zur Lösung

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

Behandle

x, s

als Konstanten

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial t} (s^{2}) = 0

\frac{\partial}{\partial t} (t^{2}) = 2 t

= x (0 - 2 t)

Vereinfache

= - 2 x t

e x p an d \frac{2 x ^{(3)} - 5 x ^{(2)} + k x + 8 k}{x + 2}

e x p an d - \frac{( 2 y + 1 ) ( 2 y ^{2} - y - 2 )}{y}

e x p an d 32

\frac{d}{d t} ((x) (t^{2} - 4 t))

e x p an d \frac{2 π x ^{2} - 44 x ^{2} + 1440 x}{9}