de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

(\partial)/(\partial x)((x-y)(1-xy))

Lösung

\frac{\partial}{\partial x} ((x - y) (1 - x y))

Lösung

1 - 2 x y + y^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} ((x - y) (1 - x y))

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x - y, g = 1 - x y

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

\frac{\partial}{\partial x} (x - y) = 1

\frac{\partial}{\partial x} (1 - x y) = - y

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

Vereinfache

1 \cdot (1 - x y) + (- y) (x - y) : 1 - 2 x y + y^{2}

= 1 - 2 x y + y^{2}

Beliebte Beispiele

derivative 7\sqrt[4]{x}

d er i v a t i v e 7 4 x

integral of sqrt(2/(2-x^2))

\int \frac{2}{2 - x ^{2}} d x

integral of (sin(x))/(cos^4(x))

\int \frac{sin ( x )}{cos ^{4} ( x )} d x

derivative (5x)/((1+x^2))

d er i v a t i v e \frac{5 x}{( 1 + x ^{2} )}

(\partial)/(\partial x)(x^2*y+(xe^x)/(y^3))

\frac{\partial}{\partial x} (x^{2} \cdot y + \frac{x e ^{x}}{y ^{3}})