(\partial)/(\partial x)(7xln(xy))

Lösung

\frac{\partial}{\partial x} (7 x ln (x y))

7 (ln (x y) + 1)

Schritte zur Lösung

\frac{\partial}{\partial x} (7 x ln (x y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 7 \frac{\partial}{\partial x} (x ln (x y))

Wende die Produktregel an:

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

f = x, g = ln (x y)

= 7 (\frac{\partial}{\partial x} (x) ln (x y) + \frac{\partial}{\partial x} (ln (x y)) x)

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

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

= 7 (1 \cdot ln (x y) + \frac{1}{x} x)

Vereinfache

7 (1 \cdot ln (x y) + \frac{1}{x} x) : 7 (ln (x y) + 1)

= 7 (ln (x y) + 1)

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