What is (\partial)/(\partial x)(-x^2y+1/y) ?

The answer to (\partial)/(\partial x)(-x^2y+1/y) is -2xy

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(\partial)/(\partial x)(-x^2y+1/y)

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

- 2 x y

Solution steps

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

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} (\frac{1}{y})

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

\frac{\partial}{\partial x} (\frac{1}{y}) = 0

= - 2 y x + 0

Simplify

= - 2 x y

\int_{1}^{3} 2^{x} d x

f (x) = x^{2} + 36

\int \frac{1}{x - 70} d x

\int \frac{9 x ^{2} - 8 x + 4}{x ^{3} + 4 x} d x

\frac{\partial}{\partial x} (6 x^{4} y - 3 x y + 2 y)

What is (\partial)/(\partial x)(-x^2y+1/y) ?
The answer to (\partial)/(\partial x)(-x^2y+1/y) is -2xy