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

The answer to (\partial)/(\partial x)(3x^2y+4xy^2) is 6yx+4y^2

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

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

6 y x + 4 y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (3 x^{2} y) = 6 y x

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

= 6 y x + 4 y^{2}

x \frac{d y}{d x} - 2 y = 2

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

\frac{d}{d x} (400 (15 - x^{2}) (3 x - 2))

\int cos (b x) d x

\int 2 x^{3} + sin (x) d x

What is (\partial)/(\partial x)(3x^2y+4xy^2) ?
The answer to (\partial)/(\partial x)(3x^2y+4xy^2) is 6yx+4y^2