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

Lösung

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

3 x^{2} - 4 x - 3 y

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x^{2} - 3 y, g = x - 2

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

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

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

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

Vereinfache

2 x (x - 2) + 1 \cdot (x^{2} - 3 y) : 3 x^{2} - 4 x - 3 y

= 3 x^{2} - 4 x - 3 y

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

\frac{\partial}{\partial x} (5 x^{3} y + 3 sin (x y))

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

\int x \cdot cos (x^{2} + 1) d x

\int \frac{3 x - 1}{4 x ^{2} - 4 x + 17} d x