What is the derivative of x*f(x) ?

The derivative of x*f(x) is 2xf

What is the first derivative of x*f(x) ?

The first derivative of x*f(x) is 2xf

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derivative of

x \cdot f (x)

2 x f

Solution steps

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

Simplify

x f x : x^{2} f

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

Treat

f

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 2 x f

\frac{d}{d x} ((x + 1)^{3} (1 - x))

\frac{1}{( s ^{2} ( s ^{2} + 4 ) )}

e^{2 t} cos (3 t - 5)

f (x) = 2 x^{4} - 11 x^{2}, at x = 2

f (x) = \frac{x ^{2} + 3 x + 2}{x ^{2} - 1}