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

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende Formel für perfekte quadratische Gleichungen an:

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

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

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

Vereinfache

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

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

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

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

e x p an d d v (2 x + 1)

\frac{\partial}{\partial x} ((z) (e^{x yz} + x y))

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