What is (\partial)/(\partial x)(4x^3y^2-4x^2+y^6+1) ?

The answer to (\partial)/(\partial x)(4x^3y^2-4x^2+y^6+1) is 12x^2y^2-8x

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(\partial)/(\partial x)(4x^3y^2-4x^2+y^6+1)

\frac{\partial}{\partial x} (4 x^{3} y^{2} - 4 x^{2} + y^{6} + 1)

12 x^{2} y^{2} - 8 x

Solution steps

\frac{\partial}{\partial x} (4 x^{3} y^{2} - 4 x^{2} + y^{6} + 1)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x^{3} y^{2}) - \frac{\partial}{\partial x} (4 x^{2}) + \frac{\partial}{\partial x} (y^{6}) + \frac{\partial}{\partial x} (1)

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

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

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

\frac{\partial}{\partial x} (1) = 0

= 12 y^{2} x^{2} - 8 x + 0 + 0

Simplify

= 12 x^{2} y^{2} - 8 x

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What is (\partial)/(\partial x)(4x^3y^2-4x^2+y^6+1) ?
The answer to (\partial)/(\partial x)(4x^3y^2-4x^2+y^6+1) is 12x^2y^2-8x