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

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

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

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

3 x^{2} + 2 y

Solution steps

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

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

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

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

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

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

Simplify

= 3 x^{2} + 2 y

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

f (x) = sin^{3} (2 x)

y = 8 x^{3} - 5 x^{2} - \frac{x}{12}

\frac{d}{d x} ((\frac{x + 3}{x - 3})^{5})

x \to \infty lim (2 - x)

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