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

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

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

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

12 x^{2} y^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (3) = 0

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

Simplify

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

\frac{d}{d n} (2^{n})

\frac{x - 1}{x + 1}

x y^{^{'}} = y + x^{2} sin (x), y (π) = 0

x \to 0 - lim (x^{2} + 4)

\frac{d}{d x} (e^{- 4 x^{6}})

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