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

Lösung

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

y (y + 3) (2 x - 2)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = x - 2

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

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

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

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

Vereinfache

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

= y (y + 3) (2 x - 2)

\int x ln (x + 5) d x

\frac{\partial}{\partial x} (ln (x^{2} + y^{5}))

\int ln (x + 2) d x

\int 7 x^{3} e^{x} d x

t an g e n t f (x) = x^{2} - 3 x + 4, at x = 1