What is (\partial)/(\partial y)(-2xy-y^4) ?

The answer to (\partial)/(\partial y)(-2xy-y^4) is -2x-4y^3

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(\partial)/(\partial y)(-2xy-y^4)

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

- 2 x - 4 y^{3}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= - 2 x - 4 y^{3}

What is (\partial)/(\partial y)(-2xy-y^4) ?
The answer to (\partial)/(\partial y)(-2xy-y^4) is -2x-4y^3