erweitern ln^{x^2}(x)(2xln(ln(x))+x/(ln(x)))

Lösung

erweitern

ln^{x^{2}} (x) (2 x ln (ln (x)) + \frac{x}{ln ( x )})

2 x ln (ln (x)) ln^{x^{2}} (x) + x ln^{x^{2} - 1} (x)

Schritte zur Lösung

ln^{x^{2}} (x) (2 x ln (ln (x)) + \frac{x}{ln ( x )})

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = ln^{x^{2}} (x), b = 2 x ln (ln (x)), c = \frac{x}{ln ( x )}

= ln^{x^{2}} (x) \cdot 2 x ln (ln (x)) + ln^{x^{2}} (x) \frac{x}{ln ( x )}

= 2 x ln^{x^{2}} (x) ln (ln (x)) + \frac{x}{ln ( x )} ln^{x^{2}} (x)

\frac{x}{ln ( x )} ln^{x^{2}} (x) = x ln^{x^{2} - 1} (x)

= 2 x ln (ln (x)) ln^{x^{2}} (x) + x ln^{x^{2} - 1} (x)

s im pl i f y (2 x - 2) (2 x + 2)

s im pl i f y (4 - y i)^{2}

e x p an d (270 + 905) c m^{3}

e x p an d (x - \frac{5}{2})^{2}

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