d/(dy)((x)(x^2+y^2-2y-10))

Lösung

\frac{d}{d y} ((x) (x^{2} + y^{2} - 2 y - 10))

x (2 y - 2)

Schritte zur Lösung

\frac{d}{d y} ((x) (x^{2} + y^{2} - 2 y - 10))

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{d}{d y} (x^{2} + y^{2} - 2 y - 10)

Wende die Summen-/Differenzregel an:

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

= x (\frac{d}{d y} (x^{2}) + \frac{d}{d y} (y^{2}) - \frac{d}{d y} (2 y) - \frac{d}{d y} (10))

\frac{d}{d y} (x^{2}) = 0

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

\frac{d}{d y} (2 y) = 2

\frac{d}{d y} (10) = 0

= x (0 + 2 y - 2 - 0)

Vereinfache

= x (2 y - 2)

e x p an d 2 (1 - 3)

s im pl i f y 2 (5 + 22)

e x p an d (t + π)^{2}

s im pl i f y (x + 1) (x + 1)

e x p an d (- \frac{8}{5} + 3) (\frac{11}{6} + 3)