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

The answer to (\partial)/(\partial x)((4x^3y^4+9)^2) is 24x^2y^4(4x^3y^4+9)

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(\partial)/(\partial x)((4x^3y^4+9)^2)

\frac{\partial}{\partial x} ((4 x^{3} y^{4} + 9)^{2})

24 x^{2} y^{4} (4 x^{3} y^{4} + 9)

Solution steps

\frac{\partial}{\partial x} ((4 x^{3} y^{4} + 9)^{2})

Treat

y

as a constant

Apply the chain rule:

2 (4 x^{3} y^{4} + 9) \frac{\partial}{\partial x} (4 x^{3} y^{4} + 9)

= 2 (4 x^{3} y^{4} + 9) \frac{\partial}{\partial x} (4 x^{3} y^{4} + 9)

\frac{\partial}{\partial x} (4 x^{3} y^{4} + 9) = 12 y^{4} x^{2}

= 2 (4 x^{3} y^{4} + 9) \cdot 12 y^{4} x^{2}

Simplify

= 24 x^{2} y^{4} (4 x^{3} y^{4} + 9)

What is (\partial)/(\partial x)((4x^3y^4+9)^2) ?
The answer to (\partial)/(\partial x)((4x^3y^4+9)^2) is 24x^2y^4(4x^3y^4+9)