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

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

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

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

y^{2} - 2 y x + y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

\int_{0}^{2} 8 e^{- 3 x} d x

x \to - 3 lim (9 - x^{2})

k = 0 \sum \infty 3 (\frac{x}{4})^{k}

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

h \to 0 lim (3 h + 6)

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