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

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

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

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

2 - 2 y x + y^{2}

Solution steps

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

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

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

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

= 2 - 2 y x + y^{2}

\int 5 cos^{2} (x) sin (2 x) d x

\frac{d}{d x} (sin (9))

x \to 0 lim (e^{x s i n (\frac{1}{x})})

y = 3

\int \frac{1}{1 - y ^{2}} d y

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