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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

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

\frac{d}{d x} (lo g_{10} (2 x))

x \to 1.75 - lim (arcsin (\frac{x}{1.75}))

\int \frac{1 + e ^{x}}{x + e ^{x}} d x

\frac{\partial}{\partial x} (x^{10} e^{x y})

x \to 2 - lim (\frac{2 x + 8}{x + 2})

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