What is (\partial)/(\partial y)(4x^3y^2+4) ?

The answer to (\partial)/(\partial y)(4x^3y^2+4) is 8x^3y

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(\partial)/(\partial y)(4x^3y^2+4)

\frac{\partial}{\partial y} (4 x^{3} y^{2} + 4)

8 x^{3} y

Solution steps

\frac{\partial}{\partial y} (4 x^{3} y^{2} + 4)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (4 x^{3} y^{2}) + \frac{\partial}{\partial y} (4)

\frac{\partial}{\partial y} (4 x^{3} y^{2}) = 8 x^{3} y

\frac{\partial}{\partial y} (4) = 0

= 8 x^{3} y + 0

Simplify

= 8 x^{3} y

What is (\partial)/(\partial y)(4x^3y^2+4) ?
The answer to (\partial)/(\partial y)(4x^3y^2+4) is 8x^3y