What is (\partial)/(\partial y)(2x^2-xy-5x+1) ?

The answer to (\partial)/(\partial y)(2x^2-xy-5x+1) is -x

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(\partial)/(\partial y)(2x^2-xy-5x+1)

\frac{\partial}{\partial y} (2 x^{2} - x y - 5 x + 1)

- x

Solution steps

\frac{\partial}{\partial y} (2 x^{2} - x y - 5 x + 1)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (2 x^{2}) - \frac{\partial}{\partial y} (x y) - \frac{\partial}{\partial y} (5 x) + \frac{\partial}{\partial y} (1)

\frac{\partial}{\partial y} (2 x^{2}) = 0

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

\frac{\partial}{\partial y} (5 x) = 0

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

= 0 - x - 0 + 0

Simplify

= - x

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What is (\partial)/(\partial y)(2x^2-xy-5x+1) ?
The answer to (\partial)/(\partial y)(2x^2-xy-5x+1) is -x