What is (\partial)/(\partial x)((4x^4y^2+9)2) ?

The answer to (\partial)/(\partial x)((4x^4y^2+9)2) is 32x^3y^2

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(\partial)/(\partial x)((4x^4y^2+9)2)

\frac{\partial}{\partial x} ((4 x^{4} y^{2} + 9) 2)

32 x^{3} y^{2}

Solution steps

\frac{\partial}{\partial x} ((4 x^{4} y^{2} + 9) \cdot 2)

Treat

y

as a constant

Take the constant out:

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

= 2 \frac{\partial}{\partial x} (4 x^{4} y^{2} + 9)

Apply the Sum/Difference Rule:

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

= 2 (\frac{\partial}{\partial x} (4 x^{4} y^{2}) + \frac{\partial}{\partial x} (9))

\frac{\partial}{\partial x} (4 x^{4} y^{2}) = 16 y^{2} x^{3}

\frac{\partial}{\partial x} (9) = 0

= 2 (16 y^{2} x^{3} + 0)

Simplify

= 32 x^{3} y^{2}

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What is (\partial)/(\partial x)((4x^4y^2+9)2) ?
The answer to (\partial)/(\partial x)((4x^4y^2+9)2) is 32x^3y^2