What is (\partial)/(\partial x)(x^3y) ?

The answer to (\partial)/(\partial x)(x^3y) is 3x^2y

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(\partial)/(\partial x)(x^3y)

\frac{\partial}{\partial x} (x^{3} y)

3 x^{2} y

Solution steps

\frac{\partial}{\partial x} (x^{3} y)

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

= y \cdot 3 x^{3 - 1}

Simplify

= 3 x^{2} y

\int (x^{8} + 1) e^{x^{9} + 9 x} d x

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

\int \frac{x ^{2} + 36 x - 9}{x ^{3} - 9 x} d x

\int_{0}^{\frac{π}{2}} tan^{2} (x) d x

What is (\partial)/(\partial x)(x^3y) ?
The answer to (\partial)/(\partial x)(x^3y) is 3x^2y