What is (\partial)/(\partial x)(-xy-x^4-y^4) ?

The answer to (\partial)/(\partial x)(-xy-x^4-y^4) is -4x^3-y

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(\partial)/(\partial x)(-xy-x^4-y^4)

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

- 4 x^{3} - y

Solution steps

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

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

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

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

\frac{\partial}{\partial x} (y^{4}) = 0

= - y - 4 x^{3} - 0

Simplify

= - 4 x^{3} - y

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What is (\partial)/(\partial x)(-xy-x^4-y^4) ?
The answer to (\partial)/(\partial x)(-xy-x^4-y^4) is -4x^3-y