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(4x^4y^2+9)

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (4 x^{4} y^{2} + 9) = 16 y^{2} x^{3}

= 2 (4 x^{4} y^{2} + 9) \cdot 16 y^{2} x^{3}

Simplify

= 32 x^{3} y^{2} (4 x^{4} y^{2} + 9)

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h \to 0 lim (\frac{( 7 + h ) - 7}{h})

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t^{2} (8 e^{2 t} - 6 sin (t))

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(4x^4y^2+9)