What is (\partial)/(\partial y)(2(y+1)x^2) ?

The answer to (\partial)/(\partial y)(2(y+1)x^2) is 2x^2

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(\partial)/(\partial y)(2(y+1)x^2)

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

2 x^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= 2 x^{2} (1 + 0)

Simplify

= 2 x^{2}

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