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

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

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

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

12 x^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (y^{2}) = 0

= 12 x^{2} + 0

Simplify

= 12 x^{2}

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