erweitern x^2sin(ln(x))(2xcos(ln(x))-xsin(ln(x)))

Lösung

erweitern

x^{2} sin (ln (x)) (2 x cos (ln (x)) - x sin (ln (x)))

2 x^{3} sin (ln (x)) cos (ln (x)) - x^{3} sin^{2} (ln (x))

Schritte zur Lösung

x^{2} sin (ln (x)) (2 x cos (ln (x)) - x sin (ln (x)))

Wende das Distributivgesetz an:

a (b - c) = ab - a c

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

= x^{2} sin (ln (x)) \cdot 2 x cos (ln (x)) - x^{2} sin (ln (x)) x sin (ln (x))

= 2 x^{2} x sin (ln (x)) cos (ln (x)) - x^{2} x sin (ln (x)) sin (ln (x))

Vereinfache

2 x^{2} x sin (ln (x)) cos (ln (x)) - x^{2} x sin (ln (x)) sin (ln (x)) : 2 x^{3} sin (ln (x)) cos (ln (x)) - x^{3} sin^{2} (ln (x))

= 2 x^{3} sin (ln (x)) cos (ln (x)) - x^{3} sin^{2} (ln (x))

e x p an d (r - e)^{3} + (r - e)^{2}

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

e x p an d \frac{14 b ^{7}}{7 b ^{5}}

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

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