What is (\partial)/(\partial x)(cos(xy)-1-sin(y)) ?

The answer to (\partial)/(\partial x)(cos(xy)-1-sin(y)) is -ysin(xy)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(cos(xy)-1-sin(y))

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

- y sin (x y)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (1) = 0

\frac{\partial}{\partial x} (sin (y)) = 0

= - sin (x y) y - 0 - 0

Simplify

= - y sin (x y)

What is (\partial)/(\partial x)(cos(xy)-1-sin(y)) ?
The answer to (\partial)/(\partial x)(cos(xy)-1-sin(y)) is -ysin(xy)