erweitern (4x^2(9x^2+2)^2)/((1+4x^2+9x^4)^3)

Lösung

erweitern

\frac{4 x ^{2} ( 9 x ^{2} + 2 ) ^{2}}{( 1 + 4 x ^{2} + 9 x ^{4} ) ^{3}}

\frac{324 x ^{6} + 144 x ^{4} + 16 x ^{2}}{729 x ^{12} + 972 x ^{10} + 675 x ^{8} + 280 x ^{6} + 75 x ^{4} + 12 x ^{2} + 1}

Schritte zur Lösung

\frac{4 x ^{2} ( 9 x ^{2} + 2 ) ^{2}}{( 1 + 4 x ^{2} + 9 x ^{4} ) ^{3}}

(1 + 4 x^{2} + 9 x^{4})^{3} = 729 x^{12} + 972 x^{10} + 675 x^{8} + 280 x^{6} + 75 x^{4} + 12 x^{2} + 1

= \frac{4 x ^{2} ( 9 x ^{2} + 2 ) ^{2}}{729 x ^{12} + 972 x ^{10} + 675 x ^{8} + 280 x ^{6} + 75 x ^{4} + 12 x ^{2} + 1}

(9 x^{2} + 2)^{2} = 81 x^{4} + 36 x^{2} + 4

= \frac{4 x ^{2} ( 81 x ^{4} + 36 x ^{2} + 4 )}{729 x ^{12} + 972 x ^{10} + 675 x ^{8} + 280 x ^{6} + 75 x ^{4} + 12 x ^{2} + 1}

Multipliziere aus

4 x^{2} (81 x^{4} + 36 x^{2} + 4) : 324 x^{6} + 144 x^{4} + 16 x^{2}

= \frac{324 x ^{6} + 144 x ^{4} + 16 x ^{2}}{729 x ^{12} + 972 x ^{10} + 675 x ^{8} + 280 x ^{6} + 75 x ^{4} + 12 x ^{2} + 1}

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

e x p an d a (- 2, - \frac{π}{3})

e x p an d \frac{10 x ^{2} + 7 x - 42}{( x - 2 ) ( x + 4 ) ( x - 1 )}

\frac{d}{d x} ((z) (sin (y z) - x - 2 y - 3 z))

e x p an d t^{2} e^{t} u (t - 1)