What is (\partial)/(\partial x)(x^3+4x^2y+2y^3) ?

The answer to (\partial)/(\partial x)(x^3+4x^2y+2y^3) is 3x^2+8xy

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(\partial)/(\partial x)(x^3+4x^2y+2y^3)

\frac{\partial}{\partial x} (x^{3} + 4 x^{2} y + 2 y^{3})

3 x^{2} + 8 x y

Solution steps

\frac{\partial}{\partial x} (x^{3} + 4 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} (4 x^{2} y) + \frac{\partial}{\partial x} (2 y^{3})

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

\frac{\partial}{\partial x} (4 x^{2} y) = 8 y x

\frac{\partial}{\partial x} (2 y^{3}) = 0

= 3 x^{2} + 8 y x + 0

Simplify

= 3 x^{2} + 8 x y

\frac{d}{d x} (\frac{1}{2 x + 2})

5 x - 4 x^{2}

f (x) = \frac{2}{x - 1}, (3, 1)

\int x e^{- 3 x} d x

\frac{d}{d y} (\frac{1}{3} y (y - 3))

What is (\partial)/(\partial x)(x^3+4x^2y+2y^3) ?
The answer to (\partial)/(\partial x)(x^3+4x^2y+2y^3) is 3x^2+8xy