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

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

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

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

8 z (4 x + 3 y)

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= z \cdot 2 (4 x + 3 y) \cdot 4

Simplify

= 8 z (4 x + 3 y)

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