(\partial)/(\partial x)(-(x-2)(y-2)(x+y-3))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

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

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

\frac{\partial}{\partial x} (x - 2) = 1

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

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

Vereinfache

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

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

\int \frac{4 x}{3 x ^{2} - 1} d x

\frac{\partial}{\partial x} (e^{- 4 x})

x \to \frac{π}{2} lim (4 sec (x))

\frac{d}{d x} (\frac{4 x}{( x - 1 ) ^{2}})

d er i v a t i v e y = 3 x - \frac{1}{x ^{2}}