What is (\partial)/(\partial y)(-1/4 (y^2+x^2)) ?

The answer to (\partial)/(\partial y)(-1/4 (y^2+x^2)) is -y/2

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(\partial)/(\partial y)(-1/4 (y^2+x^2))

\frac{\partial}{\partial y} (- \frac{1}{4} (y^{2} + x^{2}))

- \frac{y}{2}

Solution steps

\frac{\partial}{\partial y} (- \frac{1}{4} (y^{2} + x^{2}))

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{1}{4} \frac{\partial}{\partial y} (y^{2} + x^{2})

Apply the Sum/Difference Rule:

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

= - \frac{1}{4} (\frac{\partial}{\partial y} (y^{2}) + \frac{\partial}{\partial y} (x^{2}))

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

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

= - \frac{1}{4} (2 y + 0)

Simplify

- \frac{1}{4} (2 y + 0) : - \frac{y}{2}

= - \frac{y}{2}

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What is (\partial)/(\partial y)(-1/4 (y^2+x^2)) ?
The answer to (\partial)/(\partial y)(-1/4 (y^2+x^2)) is -y/2