What is the first derivative of x^2y ?

The first derivative of x^2y is 2xy

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derivative of x^2y

derivative of

x^{2} y

2 x y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 2 x y

\frac{d}{d t} (2 sin (2 t))

\frac{3 x + 1}{x ^{2} + 1}

y^{^{'}} = x + y, y (0) = 1

3 (2 z e^{z} + e^{z} z^{2})

f (x) = (x - 4)^{2}