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

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

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

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

y - 2 y x

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= y - 2 y x

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

\int \frac{1}{1 + z ^{2}} d z

f (x) = 4 (4 e^{x} - 25)^{7}

y = 15 - x^{2}, (1, 14)

\int x^{5} (2 - 5 x^{3})^{\frac{2}{3}} d x

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