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

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

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

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

2 y x + y^{2}

Solution steps

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

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^{2})

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

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

= 2 y x + y^{2}

y = x^{3}, at x = - 9

(1 + sin (x))^{- 4}

\int (\frac{1}{x} + \frac{1}{3 - x}) d x

x \to 0 lim (sin (5 x) csc (3 x))

0.02 (1 + 3 cos (t))

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