(\partial)/(\partial x)(ln(sin(xy)))

Lösung

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

y cot (x y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial x} (sin (x y)) = cos (x y) y

= \frac{1}{sin ( x y )} cos (x y) y

Vereinfache

\frac{1}{sin ( x y )} cos (x y) y : y cot (x y)

= y cot (x y)

l a pl a ce t r an s f or m sin^{2} (4 t)

\frac{\partial}{\partial x} (2 \frac{y}{x})

x \to 0 lim (e^{4 x})

l a pl a ce t r an s f or m 2 x^{2} - 3 x + 4

x \to 18 lim (- 97 x)