What is (\partial)/(\partial x)((z)(2x^3-4x^2-6y)) ?

The answer to (\partial)/(\partial x)((z)(2x^3-4x^2-6y)) is z(6x^2-8x)

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(\partial)/(\partial x)((z)(2x^3-4x^2-6y))

\frac{\partial}{\partial x} ((z) (2 x^{3} - 4 x^{2} - 6 y))

z (6 x^{2} - 8 x)

Solution steps

\frac{\partial}{\partial x} ((z) (2 x^{3} - 4 x^{2} - 6 y))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (2 x^{3} - 4 x^{2} - 6 y)

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (2 x^{3}) - \frac{\partial}{\partial x} (4 x^{2}) - \frac{\partial}{\partial x} (6 y))

\frac{\partial}{\partial x} (2 x^{3}) = 6 x^{2}

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

\frac{\partial}{\partial x} (6 y) = 0

= z (6 x^{2} - 8 x - 0)

Simplify

= z (6 x^{2} - 8 x)

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(i + k + j) (i + ik + kj + j)^{2}

x^{3} - 8 + x - 2

(10 - 4 cos (θ))^{2}

What is (\partial)/(\partial x)((z)(2x^3-4x^2-6y)) ?
The answer to (\partial)/(\partial x)((z)(2x^3-4x^2-6y)) is z(6x^2-8x)