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Beliebt Rechnen >

d/(dy)((2-x)(y-2)(3-x-y))

Lösung

\frac{d}{d y} ((2 - x) (y - 2) (3 - x - y))

Lösung

(2 - x) (5 - x - 2 y)

Schritte zur Lösung

\frac{d}{d y} ((2 - x) (y - 2) (3 - x - y))

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y - 2, g = 3 - x - y

= (2 - x) (\frac{d}{d y} (y - 2) (3 - x - y) + \frac{d}{d y} (3 - x - y) (y - 2))

\frac{d}{d y} (y - 2) = 1

\frac{d}{d y} (3 - x - y) = - 1

= (2 - x) (1 \cdot (3 - x - y) + (- 1) (y - 2))

Vereinfache

(2 - x) (1 \cdot (3 - x - y) + (- 1) (y - 2)) : (2 - x) (5 - x - 2 y)

= (2 - x) (5 - x - 2 y)

Beliebte Beispiele

integral of (x+1)/(2x+1)

\int \frac{x + 1}{2 x + 1} d x

integral of 5sin^2(x)

\int 5 sin^{2} (x) d x

derivative of sqrt(2x^2-5x+4)

\frac{d}{d x} (2 x^{2} - 5 x + 4)

integral of (x-4)^2x^2

\int (x - 4)^{2} x^{2} d x

(\partial)/(\partial x)(-3sin(2x))

\frac{\partial}{\partial x} (- 3 sin (2 x))