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

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

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

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

2 y x + y^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 y x + y^{3}

x \to \infty lim (\frac{2}{3})

\frac{d}{d x} (1 + x^{\frac{3}{2}})

\frac{\partial}{\partial x} (\frac{7}{7 x + 8 y})

\int_{- \infty}^{6} r \cdot e^{\frac{r}{3}} d r

x \to 0 + lim (x ln (2 x))

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