What is the first derivative of 3x^2y ?

The first derivative of 3x^2y is 6xy

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derivative of 3x^2y

derivative of

3 x^{2} y

6 x y

Solution steps

\frac{d}{d x} (3 x^{2} y)

Treat

y

as a constant

Take the constant out:

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

= 3 y \frac{d}{d x} (x^{2})

Apply the Power Rule:

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

= 3 y \cdot 2 x^{2 - 1}

Simplify

= 6 x y