d/(dy)((x)(y-x-xy+1))

Lösung

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

x (- x + 1)

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d x}{d y} = 0

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

\frac{d}{d y} (1) = 0

= x (1 - 0 - x + 0)

Vereinfache

= x (- x + 1)

e x p an d cos ((1 - k) π)

e x p an d \frac{( x ^{2} - 1 ) ^{5}}{10}

e x p an d x (x - a) (x - b) (x - c) + a + c

e x p an d \frac{5 ( 2 a + b )}{3 b}

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