What is (\partial)/(\partial y)(sin(y)+ysin(x)) ?

The answer to (\partial)/(\partial y)(sin(y)+ysin(x)) is cos(y)+sin(x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial y)(sin(y)+ysin(x))

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

cos (y) + sin (x)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= cos (y) + sin (x)

What is (\partial)/(\partial y)(sin(y)+ysin(x)) ?
The answer to (\partial)/(\partial y)(sin(y)+ysin(x)) is cos(y)+sin(x)