erweitern ((cos(x))/x-sin(ln(x)))^2

Lösung

erweitern

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

\frac{cos ^{2} ( x )}{x ^{2}} - \frac{2 cos ( x ) sin ( ln ( x ) )}{x} + sin^{2} (ln (x))

Schritte zur Lösung

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

Wende Formel für perfekte quadratische Gleichungen an:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = \frac{cos ( x )}{x}, b = sin (ln (x))

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

Vereinfache

(\frac{cos ( x )}{x})^{2} - 2 \cdot \frac{cos ( x )}{x} sin (ln (x)) + sin^{2} (ln (x)) : \frac{cos ^{2} ( x )}{x ^{2}} - \frac{2 cos ( x ) sin ( ln ( x ) )}{x} + sin^{2} (ln (x))

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

e x p an d (0.9) \frac{36}{( s ^{2} + 2 s + 36 )} (\frac{5}{s + 5})

e x p an d 15 e (x^{2} + 9 x) - 3 (10 + x^{9}) - lo g_{3} (8 x^{2} - 12 x)

e x p an d \frac{2}{( t + 2 ) ^{2}}

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

e x p an d (x - 1) y^{''} (x) - x y^{'} (x) + y