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

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

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

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

4 y x + 3 y^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 4 y x + 3 y^{3}

f^{^{'}} (x) = \frac{( 5 x + 1 )}{5 x}

\frac{\partial}{\partial x} (m sin (2 m x + 2 n y))

\int_{0}^{1} 2 x - x^{2} d x

\frac{\partial}{\partial x} (5 sin (x y))

\frac{d}{d x} (\frac{x ^{2}}{3 + x})

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