erweitern-4x^2e^{y^2-x^2}(1-x^2-y^2)

Lösung

erweitern

- 4 x^{2} e^{y^{2} - x^{2}} (1 - x^{2} - y^{2})

- 4 e^{y^{2} - x^{2}} x^{2} + 4 e^{y^{2} - x^{2}} x^{4} + 4 e^{y^{2} - x^{2}} x^{2} y^{2}

Schritte zur Lösung

- 4 x^{2} e^{y^{2} - x^{2}} (1 - x^{2} - y^{2})

= - 4 e^{y^{2} - x^{2}} x^{2} (1 - x^{2} - y^{2})

Setze Klammern

= (- 4 x^{2} e^{y^{2} - x^{2}}) \cdot 1 + (- 4 x^{2} e^{y^{2} - x^{2}}) (- x^{2}) + (- 4 x^{2} e^{y^{2} - x^{2}}) (- y^{2})

Wende Minus-Plus Regeln an

+ (- a) = - a, (- a) (- b) = ab

= - 4 \cdot 1 \cdot e^{y^{2} - x^{2}} x^{2} + 4 e^{y^{2} - x^{2}} x^{2} x^{2} + 4 e^{y^{2} - x^{2}} x^{2} y^{2}

Vereinfache

- 4 \cdot 1 \cdot e^{y^{2} - x^{2}} x^{2} + 4 e^{y^{2} - x^{2}} x^{2} x^{2} + 4 e^{y^{2} - x^{2}} x^{2} y^{2} : - 4 e^{y^{2} - x^{2}} x^{2} + 4 e^{y^{2} - x^{2}} x^{4} + 4 e^{y^{2} - x^{2}} x^{2} y^{2}

= - 4 e^{y^{2} - x^{2}} x^{2} + 4 e^{y^{2} - x^{2}} x^{4} + 4 e^{y^{2} - x^{2}} x^{2} y^{2}

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

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

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

e x p an d 3 sin (\frac{π}{4} (x - 5)) + 5

\frac{\partial}{\partial x} ((z) (x^{3} z^{5} + sin (y^{7} z^{5}) + 6))