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

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

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

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

4 x y^{3}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 4 x y^{3}

f (x) = x^{3} - 3 x + 2, at x = 4

y = \frac{1}{x}, y = 2 x - 1, 0, 3

x \to \infty lim (4 cos (3 x))

\int 0.55 t^{2} + 1.575 t^{4} d t

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

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