erweitern t^2cos(ln(t))*(2tsin(ln(t))+tcos(ln(t)))

Lösung

erweitern

t^{2} cos (ln (t)) \cdot (2 t sin (ln (t)) + t cos (ln (t)))

2 t^{3} cos (ln (t)) sin (ln (t)) + t^{3} cos^{2} (ln (t))

Schritte zur Lösung

t^{2} cos (ln (t)) (2 t sin (ln (t)) + t cos (ln (t)))

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = t^{2} cos (ln (t)), b = 2 t sin (ln (t)), c = t cos (ln (t))

= t^{2} cos (ln (t)) \cdot 2 t sin (ln (t)) + t^{2} cos (ln (t)) t cos (ln (t))

= 2 t^{2} t cos (ln (t)) sin (ln (t)) + t^{2} t cos (ln (t)) cos (ln (t))

Vereinfache

2 t^{2} t cos (ln (t)) sin (ln (t)) + t^{2} t cos (ln (t)) cos (ln (t)) : 2 t^{3} cos (ln (t)) sin (ln (t)) + t^{3} cos^{2} (ln (t))

= 2 t^{3} cos (ln (t)) sin (ln (t)) + t^{3} cos^{2} (ln (t))

e x p an d (sin (6 x) + cos (6 x))^{2}

e x p an d sin (θ) + (sin (θ) + cos (θ)) cos (θ)

e x p an d - cos (x) \cdot 6 (2 x + 1)^{2}

e x p an d (e^{0.5 x} - 2)^{2}

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