What is (\partial)/(\partial x)(3x^2y+6xy^3) ?

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

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(\partial)/(\partial x)(3x^2y+6xy^3)

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

6 y x + 6 y^{3}

Solution steps

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

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} (6 x y^{3})

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

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

= 6 y x + 6 y^{3}

n = 2 \sum \infty e^{\frac{1}{n}}

\frac{d}{d x} (e^{- 3 x} cos (3 x))

\frac{d}{d x} ((14 + 5 x - 3 x^{2})^{\frac{3}{4}})

\frac{d}{d x} (x^{2} sin^{8} (x) + x cos^{- 6} (x))

\int_{0}^{2 π} 6 x^{2} sin (\frac{x}{4}) d x

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