What is (\partial)/(\partial y)(y^4+5xy^3) ?

The answer to (\partial)/(\partial y)(y^4+5xy^3) is 4y^3+15xy^2

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(\partial)/(\partial y)(y^4+5xy^3)

\frac{\partial}{\partial y} (y^{4} + 5 x y^{3})

4 y^{3} + 15 x y^{2}

Solution steps

\frac{\partial}{\partial y} (y^{4} + 5 x y^{3})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (y^{4}) + \frac{\partial}{\partial y} (5 x y^{3})

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

\frac{\partial}{\partial y} (5 x y^{3}) = 15 x y^{2}

= 4 y^{3} + 15 x y^{2}

What is (\partial)/(\partial y)(y^4+5xy^3) ?
The answer to (\partial)/(\partial y)(y^4+5xy^3) is 4y^3+15xy^2