(\partial)/(\partial x)(ln(2xy+4))

Lösung

\frac{\partial}{\partial x} (ln (2 x y + 4))

\frac{y}{x y + 2}

Schritte zur Lösung

\frac{\partial}{\partial x} (ln (2 x y + 4))

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{2 x y + 4} \frac{\partial}{\partial x} (2 x y + 4)

= \frac{1}{2 x y + 4} \frac{\partial}{\partial x} (2 x y + 4)

\frac{\partial}{\partial x} (2 x y + 4) = 2 y

= \frac{1}{2 x y + 4} \cdot 2 y

Vereinfache

\frac{1}{2 x y + 4} \cdot 2 y : \frac{y}{x y + 2}

= \frac{y}{x y + 2}

\frac{\partial}{\partial y} (arctan (x + 6 y))

d er i v a t i v e y = x^{2} + 3

\int_{1}^{4} \frac{7}{x ^{2}} d x

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