(\partial)/(\partial t)((y^2)(y-t^2+1))

Lösung

\frac{\partial}{\partial t} ((y^{2}) (y - t^{2} + 1))

- 2 y^{2} t

Schritte zur Lösung

\frac{\partial}{\partial t} ((y^{2}) (y - t^{2} + 1))

Behandle

y

als Konstante

Entferne die Konstante:

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

= y^{2} \frac{\partial}{\partial t} (y - t^{2} + 1)

Wende die Summen-/Differenzregel an:

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

= y^{2} (\frac{\partial}{\partial t} (y) - \frac{\partial}{\partial t} (t^{2}) + \frac{\partial}{\partial t} (1))

\frac{\partial}{\partial t} (y) = 0

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

\frac{\partial}{\partial t} (1) = 0

= y^{2} (0 - 2 t + 0)

Vereinfache

= - 2 y^{2} t

e x p an d 1 - x ((2 - x) (1 - x))

e x p an d \frac{1}{s \cdot ( s - 1 )}

e x p an d E [x_{(t + l)} - a x_{t} - b]^{2}

e x p an d \frac{1 + 4 z ^{2}}{( 1 - 3 z ) ( 1 - 2 z ) ( 1 + 4 z )}

e x p an d \frac{y ^{3} ( x + t ) ^{2} - y ( x + t ) ^{3}}{t ( ( x + t ) ^{2} + y ^{2} )}