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}

x \to 2 lim (4 x - 5)

\int \frac{1 - x + 2 x ^{2} - x ^{3}}{x ^{5} + 2 x ^{3} + x} d x

\int_{0}^{1} 6 (1 + x)^{8} d x

\int_{2}^{3} \frac{10}{x ^{2} - 1} d x

y^{^{'}} = 10 y^{2} sin (x)

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