(\partial)/(\partial x)(axln(ax))

Lösung

\frac{\partial}{\partial x} (a x ln (a x))

a (ln (a x) + 1)

Schritte zur Lösung

\frac{\partial}{\partial x} (a x ln (a x))

Entferne die Konstante:

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

= a \frac{\partial}{\partial x} (x ln (a x))

Wende die Produktregel an:

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

f = x, g = ln (a x)

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

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

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

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

Vereinfache

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

= a (ln (a x) + 1)

\int 49 y d y

l a pl a ce t r an s f or m e^{- 4 t}

\int \frac{x}{2 x ^{2} - 5} d x

\int x^{11} x^{6} + 6 d x

t an g e n t 2 x^{2} - 3 x + 4