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

The answer to (\partial)/(\partial y)(4x^3y^3+2) is 12x^3y^2

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

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

12 x^{3} y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (4 x^{3} y^{3}) = 12 x^{3} y^{2}

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

= 12 x^{3} y^{2} + 0

Simplify

= 12 x^{3} y^{2}

x d y - y d x = (x y)^{\frac{1}{2}}

\frac{\partial}{\partial x} (6 e^{x^{5} y})

\int_{0}^{1} \frac{x - 1}{x} d x

g (x) = - 3 x^{2} + 5 x - 6

6 x

What is (\partial)/(\partial y)(4x^3y^3+2) ?
The answer to (\partial)/(\partial y)(4x^3y^3+2) is 12x^3y^2