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

The answer to (\partial)/(\partial x)(2x^2+5y^2-xy) is 4x-y

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

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

4 x - y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x^{2}) = 4 x

\frac{\partial}{\partial x} (5 y^{2}) = 0

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

= 4 x + 0 - y

Simplify

= 4 x - y

What is (\partial)/(\partial x)(2x^2+5y^2-xy) ?
The answer to (\partial)/(\partial x)(2x^2+5y^2-xy) is 4x-y