erweitern (\partial)/(\partial y)(x^2)+y^2(1+x)^3

Lösung

erweitern

\frac{\partial}{\partial y} (x^{2}) + y^{2} (1 + x)^{3}

\frac{\partial}{\partial y} (x^{2}) + y^{2} + 3 x y^{2} + 3 x^{2} y^{2} + x^{3} y^{2}

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{2}) + y^{2} (1 + x)^{3}

(1 + x)^{3} = 1 + 3 x + 3 x^{2} + x^{3}

= \frac{\partial}{\partial y} (x^{2}) + y^{2} (x^{3} + 3 x^{2} + 3 x + 1)

Multipliziere aus

y^{2} (1 + 3 x + 3 x^{2} + x^{3}) : y^{2} + 3 x y^{2} + 3 x^{2} y^{2} + x^{3} y^{2}

= \frac{\partial}{\partial y} (x^{2}) + y^{2} + 3 x y^{2} + 3 x^{2} y^{2} + x^{3} y^{2}

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

e x p an d x (3, - 1) y (0, - 5)

e x p an d e^{- \frac{6 ( x + h )}{5}} - e^{- \frac{6 x}{5}}

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

e x p an d, (5 x^{6} - 45 x^{4})