What is the derivative of x^3y ?

The derivative of x^3y is 3x^2y

What is the first derivative of x^3y ?

The first derivative of x^3y is 3x^2y

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derivative of

x^{3} y

3 x^{2} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

= y \frac{d}{d 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