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

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

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

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

4 y x + 3 y^{2}

Solution steps

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

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^{2})

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

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

= 4 y x + 3 y^{2}

n = 1 \sum \infty (\frac{- 1}{2})^{n}

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

2 e^{- t} cos (2 t)

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

n = 0 \sum \infty \frac{( 1 0 ^{2 n} )}{n !}

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