What is (\partial)/(\partial x)(4x^3y^3-18y-x) ?

The answer to (\partial)/(\partial x)(4x^3y^3-18y-x) is 12x^2y^3-1

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(\partial)/(\partial x)(4x^3y^3-18y-x)

\frac{\partial}{\partial x} (4 x^{3} y^{3} - 18 y - x)

12 x^{2} y^{3} - 1

Solution steps

\frac{\partial}{\partial x} (4 x^{3} y^{3} - 18 y - x)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x^{3} y^{3}) - \frac{\partial}{\partial x} (18 y) - \frac{\partial}{\partial x} (x)

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

\frac{\partial}{\partial x} (18 y) = 0

\frac{\partial}{\partial x} (x) = 1

= 12 y^{3} x^{2} - 0 - 1

Simplify

= 12 x^{2} y^{3} - 1

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What is (\partial)/(\partial x)(4x^3y^3-18y-x) ?
The answer to (\partial)/(\partial x)(4x^3y^3-18y-x) is 12x^2y^3-1