d/(dy)((x)(x^4y^3+8x^2y))

Lösung

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

x (3 x^{4} y^{2} + 8 x^{2})

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d y} (8 x^{2} y) = 8 x^{2}

= x (3 x^{4} y^{2} + 8 x^{2})

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

e x p an d \frac{x}{( x - 1 ) ( x - 0.7 + 0.9 j ) ( z - 0.7 - 0.9 j )}

e x p an d x ((x + 1) \cdot (x + 2))

e x p an d \frac{( s + 5 )}{s ( s ^{2} + 2 s + 10 )}

e x p an d (\frac{a}{1 - b cos ( θ )})^{2}