erweitern (240x(3x^4-10*x^2+3))/((1+x^2)^6)

Lösung

erweitern

\frac{240 \cdot x ( 3 \cdot x ^{4} - 10 \cdot x ^{2} + 3 )}{( 1 + x ^{2} ) ^{6}}

\frac{720 x ^{5} - 2400 x ^{3} + 720 x}{1 + 6 x ^{2} + 15 x ^{4} + 20 x ^{6} + 15 x ^{8} + 6 x ^{10} + x ^{12}}

Schritte zur Lösung

\frac{240 x ( 3 x ^{4} - 10 x ^{2} + 3 )}{( 1 + x ^{2} ) ^{6}}

(1 + x^{2})^{6} = 1 + 6 x^{2} + 15 x^{4} + 20 x^{6} + 15 x^{8} + 6 x^{10} + x^{12}

= \frac{240 x ( 3 x ^{4} - 10 x ^{2} + 3 )}{1 + 6 x ^{2} + 15 x ^{4} + 20 x ^{6} + 15 x ^{8} + 6 x ^{10} + x ^{12}}

Multipliziere aus

240 x (3 x^{4} - 10 x^{2} + 3) : 720 x^{5} - 2400 x^{3} + 720 x

= \frac{720 x ^{5} - 2400 x ^{3} + 720 x}{1 + 6 x ^{2} + 15 x ^{4} + 20 x ^{6} + 15 x ^{8} + 6 x ^{10} + x ^{12}}

\frac{d ^{2}}{d x ^{2}} ((y) (x - \frac{1}{2} sin (x)))

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

e x p an d \frac{s + 8}{( s + 3 ) ( s + 6 ) ( s + 10 )}

s im pl i f y (cos (x)) (1 - sin (x))

e x p an d \frac{8}{( x + 2 ) ( x - 2 )}