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

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

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

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

12 x^{2} y^{3}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

\int (1 + \frac{1}{x})^{3} \cdot (\frac{1}{x ^{2}}) d x

\frac{d}{d x} (x^{5^{x}})

\int \frac{9 + u}{u} d u

\int \frac{u}{u ^{2} - 1} d u

\frac{\partial}{\partial x} (sin (4 x - 6 y))

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