erweitern 4(x^2+y^2)(2x+2y(dy)/(dx))

Lösung

erweitern

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

8 x^{3} + 8 x^{2} y \frac{d y}{d x} + 8 x y^{2} + 8 y^{3} \frac{d y}{d x}

Schritte zur Lösung

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

Multipliziere aus

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

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

Multipliziere aus

4 (2 x^{3} + 2 x^{2} y \frac{d y}{d x} + 2 x y^{2} + 2 y^{3} \frac{d y}{d x}) : 8 x^{3} + 8 x^{2} y \frac{d y}{d x} + 8 x y^{2} + 8 y^{3} \frac{d y}{d x}

= 8 x^{3} + 8 x^{2} y \frac{d y}{d x} + 8 x y^{2} + 8 y^{3} \frac{d y}{d x}

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

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

s im pl i f y e^{- i \cdot x} \cdot (6 + e^{i \cdot x} + e^{- i \cdot x})

e x p an d d (cos (x) + 2)

e x p an d csc^{2} (x) (1 - sin (x))