erweitern-(40(-34x^4-343x^2-208))/((x^2-16)^{11)}

Lösung

erweitern

- \frac{40 ( - 34 x ^{4} - 343 x ^{2} - 208 )}{( x ^{2} - 16 ) ^{11}}

- \frac{- 1360 x ^{4} - 13720 x ^{2} - 8320}{x ^{22} - 176 x ^{20} + 14080 x ^{18} - 675840 x ^{16} + 21626880 x ^{14} - 484442112 x ^{12} + 7751073792 x ^{10} - 88583700480 x ^{8} + 1 6 ^{8} \cdot 165 x ^{6} - 1 6 ^{9} \cdot 55 x ^{4} + 1 6 ^{10} \cdot 11 x ^{2} - 1 6 ^{11}}

Schritte zur Lösung

- \frac{40 ( - 34 x ^{4} - 343 x ^{2} - 208 )}{( x ^{2} - 16 ) ^{11}}

(x^{2} - 16)^{11} = x^{22} - 176 x^{20} + 14080 x^{18} - 675840 x^{16} + 21626880 x^{14} - 484442112 x^{12} + 7751073792 x^{10} - 88583700480 x^{8} + 1 6^{8} \cdot 165 x^{6} - 1 6^{9} \cdot 55 x^{4} + 1 6^{10} \cdot 11 x^{2} - 1 6^{11}

= - \frac{40 ( - 34 x ^{4} - 343 x ^{2} - 208 )}{x ^{22} - 176 x ^{20} + 14080 x ^{18} - 675840 x ^{16} + 21626880 x ^{14} - 484442112 x ^{12} + 7751073792 x ^{10} - 88583700480 x ^{8} + 1 6 ^{8} \cdot 165 x ^{6} - 1 6 ^{9} \cdot 55 x ^{4} + 1 6 ^{10} \cdot 11 x ^{2} - 1 6 ^{11}}

Multipliziere aus

40 (- 34 x^{4} - 343 x^{2} - 208) : - 1360 x^{4} - 13720 x^{2} - 8320

= - \frac{- 1360 x ^{4} - 13720 x ^{2} - 8320}{x ^{22} - 176 x ^{20} + 14080 x ^{18} - 675840 x ^{16} + 21626880 x ^{14} - 484442112 x ^{12} + 7751073792 x ^{10} - 88583700480 x ^{8} + 1 6 ^{8} \cdot 165 x ^{6} - 1 6 ^{9} \cdot 55 x ^{4} + 1 6 ^{10} \cdot 11 x ^{2} - 1 6 ^{11}}

e x p an d \frac{4 ( 3 x ^{2} ( 3 y ^{2} + 1 ) ^{2} - 24 x ^{6} y )}{( 3 y ^{2} + 1 ) ^{3}}

s im pl i f y 10 (5 - 5)

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

s im pl i f y (x + 9 - x)^{2}

s im pl i f y \frac{1}{2} (4 + 3 x + 4 - 8 x + 5 x^{2})