erweitern 3(ln(x+1)+x/(x+1))(x+1)^{3x}

Lösung

erweitern

3 (ln (x + 1) + \frac{x}{x + 1}) (x + 1)^{3 x}

3 ln (x + 1) (x + 1)^{3 x} + 3 x (x + 1)^{3 x - 1}

Schritte zur Lösung

3 (ln (x + 1) + \frac{x}{x + 1}) (x + 1)^{3 x}

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = 3 (x + 1)^{3 x}, b = ln (x + 1), c = \frac{x}{x + 1}

= 3 (x + 1)^{3 x} ln (x + 1) + 3 (x + 1)^{3 x} \frac{x}{x + 1}

= 3 ln (x + 1) (x + 1)^{3 x} + 3 \cdot \frac{x}{x + 1} (x + 1)^{3 x}

3 \cdot \frac{x}{x + 1} (x + 1)^{3 x} = 3 x (x + 1)^{3 x - 1}

= 3 ln (x + 1) (x + 1)^{3 x} + 3 x (x + 1)^{3 x - 1}

e x p an d (3 x + 2 y + 1)^{2}

e x p an d (10) (cos (t) + i sin (t))

e x p an d (cos^{4} (t) - \frac{2}{3} cos^{6} (t)) cos (2 t)

e x p an d d x (x - 3) (y - 4)

s im pl i f y i (x + y i)^{2}