(\partial)/(\partial x)((x+y)ln(x+y))

Lösung

\frac{\partial}{\partial x} ((x + y) ln (x + y))

ln (x + y) + 1

Schritte zur Lösung

\frac{\partial}{\partial x} ((x + y) ln (x + y))

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x + y, g = ln (x + y)

= \frac{\partial}{\partial x} (x + y) ln (x + y) + \frac{\partial}{\partial x} (ln (x + y)) (x + y)

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

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

= 1 \cdot ln (x + y) + \frac{1}{x + y} (x + y)

Vereinfache

1 \cdot ln (x + y) + \frac{1}{x + y} (x + y) : ln (x + y) + 1

= ln (x + y) + 1

x \to 4 + lim (x + 1)

\int e^{3 x} \cdot sin (2 x) d x

\frac{d y}{d t} = k y^{2}

\int e^{i t x} d x

\int (ln (x))^{4} d x