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

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

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

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

12 x^{3} y^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 4 x^{3} \cdot 3 y^{3 - 1}

Simplify

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

y = 2 x^{2} - 1, (0, 1)

x \to 4 lim (4 x^{2} + 5 x + 1)

\frac{d}{d x} (3 x + 3)

x \to 0 lim (\frac{x}{sin ( \frac{x}{4} )})

\frac{d}{d x} (e^{x} - 2 - x)

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