erweitern t^2(at+b)e^t

Lösung

erweitern

t^{2} (a t + b) e^{t}

e^{t} t^{3} a + e^{t} t^{2} b

Schritte zur Lösung

t^{2} (a t + b) e^{t}

= e^{t} t^{2} (t a + b)

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = t^{2} e^{t}, b = a t, c = b

= t^{2} e^{t} a t + t^{2} e^{t} b

= e^{t} t^{2} t a + e^{t} t^{2} b

e^{t} t^{2} t a = e^{t} t^{3} a

= e^{t} t^{3} a + e^{t} t^{2} b

e x p an d \frac{2 ( 3Δ x - 2 x - 1 )}{Δ x ( 1 - 2 x - 2Δ x ) ( 1 - 2 x )}

e x p an d \frac{6 x ^{2} + 7 x - 3}{x ^{2} ( x + 5 )}

\frac{\partial}{\partial t} ((x) (a x - b x y))

e x p an d (a \cdot b) + (c \cdot d) + (e \cdot f) + (g \cdot h)

e x p an d \frac{20 x ( x + 6 )}{3}