What is (\partial)/(\partial x)(4x^3+2xy+1) ?

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

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(\partial)/(\partial x)(4x^3+2xy+1)

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

12 x^{2} + 2 y

Solution steps

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

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} (2 x y) + \frac{\partial}{\partial x} (1)

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

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

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

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

Simplify

= 12 x^{2} + 2 y

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