(\partial)/(\partial y)(ln(sqrt(1+xy)))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{1 + x y} \cdot \frac{x}{2 1 + x y} : \frac{x}{2 ( 1 + x y )}

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

\int \frac{1}{x ^{2} + 4 x + 1} d x

\frac{\partial}{\partial x} (5 x y (9 - x - y))

d er i v a t i v e e^{x} - 3 x

\frac{\partial}{\partial x} (8)

3 t \frac{d y}{d t} + y = t