What is (\partial)/(\partial x)(ln(sin(xy))) ?

The answer to (\partial)/(\partial x)(ln(sin(xy))) is ycot(xy)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

y cot (x y)

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\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

Simplify

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

= y cot (x y)

What is (\partial)/(\partial x)(ln(sin(xy))) ?
The answer to (\partial)/(\partial x)(ln(sin(xy))) is ycot(xy)