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

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

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

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

4 x y^{3}

Solution steps

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

\frac{\partial}{\partial y} (x^{2}) = 0

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

= 0 + 4 x y^{3}

Simplify

= 4 x y^{3}

\int_{1}^{x} \frac{1}{t} d t

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

y = \frac{x - x}{x ^{2}}

ln (1 + 3 x)

\frac{d y}{d x} + 2 x y = y + 6 x - 3

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