What is (\partial)/(\partial y)(27xy^2+8y^3) ?

The answer to (\partial)/(\partial y)(27xy^2+8y^3) is 54xy+24y^2

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(\partial)/(\partial y)(27xy^2+8y^3)

\frac{\partial}{\partial y} (27 x y^{2} + 8 y^{3})

54 x y + 24 y^{2}

Solution steps

\frac{\partial}{\partial y} (27 x y^{2} + 8 y^{3})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (27 x y^{2}) + \frac{\partial}{\partial y} (8 y^{3})

\frac{\partial}{\partial y} (27 x y^{2}) = 54 x y

\frac{\partial}{\partial y} (8 y^{3}) = 24 y^{2}

= 54 x y + 24 y^{2}

What is (\partial)/(\partial y)(27xy^2+8y^3) ?
The answer to (\partial)/(\partial y)(27xy^2+8y^3) is 54xy+24y^2