erweitern e^{(y^3)/3}[3x^2y^2dx+(2x^3y+x^3y^4)dy]

Lösung

erweitern

e^{\frac{y ^{3}}{3}} [3 x^{2} y^{2} d x + (2 x^{3} y + x^{3} y^{4}) d y]

3 e^{\frac{y ^{3}}{3}} y^{2} x^{2} d x + 2 e^{\frac{y ^{3}}{3}} y x^{3} d y + e^{\frac{y ^{3}}{3}} y^{4} x^{3} d y

Schritte zur Lösung

e^{\frac{y ^{3}}{3}} (3 x^{2} y^{2} d x + (2 x^{3} y + x^{3} y^{4}) d y)

Multipliziere aus

3 x^{2} y^{2} d x + (2 x^{3} y + x^{3} y^{4}) d y : 3 x^{2} y^{2} d x + 2 y x^{3} d y + y^{4} x^{3} d y

= e^{\frac{y ^{3}}{3}} (y^{4} x^{3} d y + 3 y^{2} x^{2} d x + 2 y x^{3} d y)

= e^{\frac{y ^{3}}{3}} (3 y^{2} x^{2} d x + 2 y x^{3} d y + y^{4} x^{3} d y)

Setze Klammern

= e^{\frac{y ^{3}}{3}} \cdot 3 x^{2} y^{2} d x + e^{\frac{y ^{3}}{3}} \cdot 2 y x^{3} d y + e^{\frac{y ^{3}}{3}} y^{4} x^{3} d y

= 3 e^{\frac{y ^{3}}{3}} y^{2} x^{2} d x + 2 e^{\frac{y ^{3}}{3}} y x^{3} d y + e^{\frac{y ^{3}}{3}} y^{4} x^{3} d y

e x p an d \frac{( 16 m ^{3} + n ^{2} ) ^{2}}{16}

e x p an d (4 - \frac{1}{n})^{6}

e x p an d (4 - \frac{1}{n})^{7}

e x p an d (- 2, - 3) (3 x + 5 y - 12 = 0)

e x p an d - csc (x) (sin (4 x) - 2 sin (3 x) cos (x))