d/(dy)((x)(y-{p}(x)x))

Lösung

\frac{d}{d y} ((x) (y - p (x) x))

x (1 - x \frac{d}{d y} (p (x)))

Schritte zur Lösung

\frac{d}{d y} ((x) (y - p (x) x))

Behandle

x

als Konstante

Entferne die Konstante:

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

= x \frac{d}{d y} (y - p (x) x)

Wende die Summen-/Differenzregel an:

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

= x (\frac{d y}{d y} - \frac{d}{d y} (p (x) x))

\frac{d y}{d y} = 1

\frac{d}{d y} (p (x) x) = x \frac{d}{d y} (p (x))

= x (1 - x \frac{d}{d y} (p (x)))

e x p an d (2 + \frac{y}{x ^{2}}) d y

e x p an d \frac{14 x ^{3}}{( x - 3 ) ^{2}}

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

e x p an d \frac{( 0.2 ( 0.01 x ^{2} + 120 ) )}{x}

e x p an d 3 (- 7 x + 4 y = - 8)