What is (\partial)/(\partial x)(xycos(3x)+e^{xy}) ?

The answer to (\partial)/(\partial x)(xycos(3x)+e^{xy}) is y(cos(3x)-3xsin(3x))+e^{xy}y

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(xycos(3x)+e^{xy})

\frac{\partial}{\partial x} (x y cos (3 x) + e^{x y})

y (cos (3 x) - 3 x sin (3 x)) + e^{x y} y

Solution steps

\frac{\partial}{\partial x} (x y cos (3 x) + e^{x y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x y cos (3 x)) + \frac{\partial}{\partial x} (e^{x y})

\frac{\partial}{\partial x} (x y cos (3 x)) = y (cos (3 x) - 3 x sin (3 x))

\frac{\partial}{\partial x} (e^{x y}) = e^{x y} y

= y (cos (3 x) - 3 x sin (3 x)) + e^{x y} y

What is (\partial)/(\partial x)(xycos(3x)+e^{xy}) ?
The answer to (\partial)/(\partial x)(xycos(3x)+e^{xy}) is y(cos(3x)-3xsin(3x))+e^{xy}y