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

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

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

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

8 x y^{3}

Solution steps

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

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} (4)

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

\frac{\partial}{\partial y} (4) = 0

= 8 x y^{3} - 0

Simplify

= 8 x y^{3}

\int x^{3} (x^{2} + 1)^{8} d x

\frac{d}{d z} (x e^{\frac{y}{z}})

\int \frac{1}{( a x + b ) ^{4}} d x

\int_{0}^{1} π (y^{2} - y^{4}) d y

\frac{\partial}{\partial x} (z^{2} + 5 x^{2} + y^{2})

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