erweitern ((1-x^2)sin(x)-xcos(2x))/(tan(x^3))

Lösung

erweitern

\frac{( 1 - x ^{2} ) sin ( x ) - x cos ( 2 x )}{tan ( x ^{3} )}

\frac{sin ( x )}{tan ( x ^{3} )} - \frac{x ^{2} sin ( x )}{tan ( x ^{3} )} - \frac{x cos ( 2 x )}{tan ( x ^{3} )}

Schritte zur Lösung

\frac{( 1 - x ^{2} ) sin ( x ) - x cos ( 2 x )}{tan ( x ^{3} )}

Multipliziere aus

(1 - x^{2}) sin (x) - x cos (2 x) : sin (x) - x^{2} sin (x) - x cos (2 x)

= \frac{sin ( x ) - x ^{2} sin ( x ) - x cos ( 2 x )}{tan ( x ^{3} )}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{sin ( x ) - x ^{2} sin ( x ) - x cos ( 2 x )}{tan ( x ^{3} )} = \frac{sin ( x )}{tan ( x ^{3} )} - \frac{x ^{2} sin ( x )}{tan ( x ^{3} )} - \frac{x cos ( 2 x )}{tan ( x ^{3} )}

= \frac{sin ( x )}{tan ( x ^{3} )} - \frac{x ^{2} sin ( x )}{tan ( x ^{3} )} - \frac{x cos ( 2 x )}{tan ( x ^{3} )}

e x p an d y (10, 5, - 2)

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

e x p an d - x^{2} (cot (3 y) + x^{3} y sin (3 y) d y)

e x p an d (x + 4) \cdot ln (\frac{x + 12}{x + 4})

s im pl i f y x d (y + y_{2}) d y_{2} + (1 - 2 y_{2}) d y