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

The answer to (\partial)/(\partial y)(x^2+4y^2) is 8y

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

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

8 y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (4 y^{2}) = 8 y

= 0 + 8 y

Simplify

= 8 y

\frac{d y}{d x} = y + e^{x}

\int \frac{4 - x ^{2}}{x ^{2}} d x

\int_{0}^{11} x 11 - x d x

x \to 3 lim (5 x^{3})

x \to - 1 lim (e^{x + 1})

What is (\partial)/(\partial y)(x^2+4y^2) ?
The answer to (\partial)/(\partial y)(x^2+4y^2) is 8y