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

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

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

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

4 x

Solution steps

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

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} (2 y^{2})

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

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

= 4 x + 0

Simplify

= 4 x

\frac{d}{d x} (\frac{x}{9 - 4 x})

x^{2} y^{^{''}} - x (x + 2) y^{^{'}} + (x + 2) y = 2 x^{3}

y^{^{''}} + 9 y = - 24 sin (3 t)

x \to - 3 lim (x^{2} + 2 x - 3)

\int (x + 3) x + 3 d x

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