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

The answer to (\partial)/(\partial y)(2xy^4+2) is 8xy^3

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

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

8 x y^{3}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (2 x y^{4}) = 8 x y^{3}

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

= 8 x y^{3} + 0

Simplify

= 8 x y^{3}

x \to 0 lim (\frac{1}{2 x})

\frac{d}{d x} (\frac{x ^{3} - x + 3 x ^{\frac{3}{2}}}{x})

\frac{d}{d x} (\frac{x}{1 - ln ( x )})

y^{^{'}} = 0.002 y - 200

\int_{\frac{1}{2}}^{1} \frac{4 y + 5}{y ^{2} + y} d y

What is (\partial)/(\partial y)(2xy^4+2) ?
The answer to (\partial)/(\partial y)(2xy^4+2) is 8xy^3