What is (\partial)/(\partial x)(xe^y+x^4y+y^3) ?

The answer to (\partial)/(\partial x)(xe^y+x^4y+y^3) is e^y+4x^3y

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(xe^y+x^4y+y^3)

\frac{\partial}{\partial x} (x e^{y} + x^{4} y + y^{3})

e^{y} + 4 x^{3} y

Solution steps

\frac{\partial}{\partial x} (x e^{y} + x^{4} y + y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x e^{y}) + \frac{\partial}{\partial x} (x^{4} y) + \frac{\partial}{\partial x} (y^{3})

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

\frac{\partial}{\partial x} (x^{4} y) = 4 y x^{3}

\frac{\partial}{\partial x} (y^{3}) = 0

= e^{y} + 4 y x^{3} + 0

Simplify

= e^{y} + 4 x^{3} y

What is (\partial)/(\partial x)(xe^y+x^4y+y^3) ?
The answer to (\partial)/(\partial x)(xe^y+x^4y+y^3) is e^y+4x^3y