What is (\partial)/(\partial x)(x^3+x^2y^2+y^3) ?

The answer to (\partial)/(\partial x)(x^3+x^2y^2+y^3) is 3x^2+2xy^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(x^3+x^2y^2+y^3)

\frac{\partial}{\partial x} (x^{3} + x^{2} y^{2} + y^{3})

3 x^{2} + 2 x y^{2}

Solution steps

\frac{\partial}{\partial x} (x^{3} + x^{2} y^{2} + y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{3}) + \frac{\partial}{\partial x} (x^{2} y^{2}) + \frac{\partial}{\partial x} (y^{3})

\frac{\partial}{\partial x} (x^{3}) = 3 x^{2}

\frac{\partial}{\partial x} (x^{2} y^{2}) = 2 y^{2} x

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

= 3 x^{2} + 2 y^{2} x + 0

Simplify

= 3 x^{2} + 2 x y^{2}

What is (\partial)/(\partial x)(x^3+x^2y^2+y^3) ?
The answer to (\partial)/(\partial x)(x^3+x^2y^2+y^3) is 3x^2+2xy^2