What is (\partial)/(\partial y)(2x(3y^2+2x^2)) ?

The answer to (\partial)/(\partial y)(2x(3y^2+2x^2)) is 12xy

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(\partial)/(\partial y)(2x(3y^2+2x^2))

\frac{\partial}{\partial y} (2 x (3 y^{2} + 2 x^{2}))

12 x y

Solution steps

\frac{\partial}{\partial y} (2 x (3 y^{2} + 2 x^{2}))

Treat

x

as a constant

Take the constant out:

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

= 2 x \frac{\partial}{\partial y} (3 y^{2} + 2 x^{2})

Apply the Sum/Difference Rule:

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

= 2 x (\frac{\partial}{\partial y} (3 y^{2}) + \frac{\partial}{\partial y} (2 x^{2}))

\frac{\partial}{\partial y} (3 y^{2}) = 6 y

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

= 2 x (6 y + 0)

Simplify

= 12 x y

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What is (\partial)/(\partial y)(2x(3y^2+2x^2)) ?
The answer to (\partial)/(\partial y)(2x(3y^2+2x^2)) is 12xy