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

(\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

t an g e n t f (x) = \frac{2}{x - 1}, (3, 1)

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

\frac{d}{d x} (x^{l n (x^{2} + 1)})

\frac{d ^{2}}{d x ^{2}} (e^{s i n (x)})

\frac{d}{d x} ((sin (y)) x^{2})

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