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

The answer to (\partial)/(\partial x)(4x^2y^3+2) is 8xy^3

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

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

8 x y^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (4 x^{2} y^{3}) = 8 y^{3} x

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

= 8 y^{3} x + 0

Simplify

= 8 x y^{3}

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x^{2}

\frac{d}{d x} (\frac{5 x - 1}{( 6 x ^{2} - 2 ) ^{2}})

\frac{d}{d x} (ln (\frac{x}{4}) \cdot (x - 4))

What is (\partial)/(\partial x)(4x^2y^3+2) ?
The answer to (\partial)/(\partial x)(4x^2y^3+2) is 8xy^3