What is (\partial)/(\partial x)((4x+6y)^4) ?

The answer to (\partial)/(\partial x)((4x+6y)^4) is 16(4x+6y)^3

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(\partial)/(\partial x)((4x+6y)^4)

\frac{\partial}{\partial x} ((4 x + 6 y)^{4})

16 (4 x + 6 y)^{3}

Solution steps

\frac{\partial}{\partial x} ((4 x + 6 y)^{4})

Treat

y

as a constant

Apply the chain rule:

4 (4 x + 6 y)^{3} \frac{\partial}{\partial x} (4 x + 6 y)

= 4 (4 x + 6 y)^{3} \frac{\partial}{\partial x} (4 x + 6 y)

\frac{\partial}{\partial x} (4 x + 6 y) = 4

= 4 (4 x + 6 y)^{3} \cdot 4

Simplify

= 16 (4 x + 6 y)^{3}

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What is (\partial)/(\partial x)((4x+6y)^4) ?
The answer to (\partial)/(\partial x)((4x+6y)^4) is 16(4x+6y)^3