What is the derivative of x^2f(x) ?

The derivative of x^2f(x) is 3x^2f

What is the first derivative of x^2f(x) ?

The first derivative of x^2f(x) is 3x^2f

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derivative of

x^{2} f (x)

3 x^{2} f

Solution steps

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

Simplify

x^{2} f x : x^{3} f

= \frac{d}{d x} (x^{3} f)

Treat

f

as a constant

Take the constant out:

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

= f \frac{d}{d x} (x^{3})

Apply the Power Rule:

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

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

Simplify

= 3 x^{2} f

What is the derivative of x^2f(x) ?
The derivative of x^2f(x) is 3x^2f
What is the first derivative of x^2f(x) ?
The first derivative of x^2f(x) is 3x^2f