d/(dy)((x)(x^2+y^2-4x+10y-12))

Lösung

\frac{d}{d y} ((x) (x^{2} + y^{2} - 4 x + 10 y - 12))

x (2 y + 10)

Schritte zur Lösung

\frac{d}{d y} ((x) (x^{2} + y^{2} - 4 x + 10 y - 12))

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{d}{d y} (x^{2} + y^{2} - 4 x + 10 y - 12)

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} (4 x) + \frac{d}{d y} (10 y) - \frac{d}{d y} (12))

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

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

\frac{d}{d y} (4 x) = 0

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

\frac{d}{d y} (12) = 0

= x (0 + 2 y - 0 + 10 - 0)

Vereinfache

= x (2 y + 10)

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

e x p an d \frac{8 ( 2 ( - 1 ) ^{n} - π ^{2} ( - 1 ) ^{n} n ^{2} - 2 )}{π n ^{3}}

e x p an d \frac{1}{\frac{16 x ^{2}}{n ^{2}} - \frac{8 x}{n} + 1}

e x p an d \frac{37.68}{3}

e x p an d \frac{20 ( 110 - 12010 )}{3}