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

The derivative of x^2*{f}(x) is 2x{f}(x)+derivative of {f}(x)x^2

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

The first derivative of x^2*{f}(x) is 2x{f}(x)+derivative of {f}(x)x^2

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = f (x)

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

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

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

\frac{d}{d x} (e^{- arcsinh (\frac{x}{2})})

\frac{x}{6 x - 6}

\frac{d}{d x} (∣ x ∣^{3})

\int \frac{1}{( 4 x - x ^{2} ) ^{3}} d x

\int e^{- t (a + s)} d t

What is the derivative of x^2*{f}(x) ?
The derivative of x^2*{f}(x) is 2x{f}(x)+derivative of {f}(x)x^2
What is the first derivative of x^2*{f}(x) ?
The first derivative of x^2*{f}(x) is 2x{f}(x)+derivative of {f}(x)x^2