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

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

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

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

x^{2} + 12 x y^{3}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= x^{2} + 12 x y^{3}

\frac{d}{d x} (7 x^{\frac{3}{2}})

\int \frac{x}{x ln ( x )} d x

y^{^{'}} = - y^{2} t - y^{2} t^{2}, y (0) = 3

x \to \frac{1}{2} - lim (\frac{1}{2 x - 1})

\frac{d}{d x} (ln (\frac{x ^{2}}{x + 1}))

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