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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e f (x) = 6 x^{\frac{1}{5}} (x^{3} - 8)

x \to 1 lim (+ \frac{1}{x - 1})

\int e^{θ} cos (θ) d θ

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

\int \frac{1}{e ^{x} - 3} d x