What is (\partial)/(\partial x)(xy-5x^2y) ?

The answer to (\partial)/(\partial x)(xy-5x^2y) is y-10yx

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(\partial)/(\partial x)(xy-5x^2y)

\frac{\partial}{\partial x} (x y - 5 x^{2} y)

y - 10 y x

Solution steps

\frac{\partial}{\partial x} (x y - 5 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} (5 x^{2} y)

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

\frac{\partial}{\partial x} (5 x^{2} y) = 10 y x

= y - 10 y x

\frac{d ^{2}}{d x ^{2}} f (x) = 5 x^{3} + 12 x^{2} + 8 x + 22

\frac{\partial}{\partial x} (4 (y - 1) (x - 4)^{3})

\int y e^{0.2 y} d y

\int_{0}^{π} 3 tan (\frac{x}{3}) d x

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

What is (\partial)/(\partial x)(xy-5x^2y) ?
The answer to (\partial)/(\partial x)(xy-5x^2y) is y-10yx