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

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

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

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

4 x^{3} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 4 x^{3} y

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