erweitern (3x^2+3y^2(dy)/(dx))(x^2+y^2)

Lösung

erweitern

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

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

Schritte zur Lösung

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

Wende Ausklammerungsregel an (VANI):

(a + b) (c + d) = a c + a d + b c + b d

a = 3 x^{2}, b = 3 y^{2} \frac{d y}{d x}, c = x^{2}, d = y^{2}

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

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

Vereinfache

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

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

e x p an d \frac{2 ( 2 n + 3 ) \cdot ( 5 n + 3 )}{3 ( 5 n + 8 ) \cdot ( 2 n + 1 )}

e x p an d f (x) (sin (\frac{x}{2}) = 2 + cos (x))

e x p an d x + 8 x + 16

e x p an d (cos (x) + a sin (x))^{2}

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