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

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

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

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

8 y x + 2 y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 8 y x + 2 y^{2}

sin (cos (x))

\int \frac{1}{3 x ( 4 + x )} d x

\int - 3 x^{2} e^{x} d x

\frac{\partial}{\partial x} (x + 3 lo g_{10} (x) - y^{2})

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