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

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

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

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

8 x y^{3}

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 2 x \cdot 4 y^{4 - 1}

Simplify

= 8 x y^{3}

f (x) = (x)^{(3)} e^{(3 x)}

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

y^{^{'}} + 6 y = 2 t + 3, y (0) = 1

\int \frac{5 x + 1}{x ^{2} - 1} d x

x \to 5 - lim (\frac{x}{x - 5})

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