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

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

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

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

12 y^{2} x^{2}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= 4 y^{2} \cdot 3 x^{3 - 1}

Simplify

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

\int_{0}^{1} (x + 1) (x^{2} + 2 x)^{5} d x

\int \frac{- 1800 x}{25 - x ^{2}} d x

t^{2} cos (3 t)

x \to 13 lim (x^{4} - 10 x^{2} - 20)

x \to \infty lim (x e^{(\frac{1}{x})})

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