What is the derivative of x^2ln(1/x) ?

The derivative of x^2ln(1/x) is -2xln(x)-x

What is the first derivative of x^2ln(1/x) ?

The first derivative of x^2ln(1/x) is -2xln(x)-x

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\frac{d}{d x} (x^{2} ln (\frac{1}{x}))

- 2 x ln (x) - x

Solution steps

\frac{d}{d x} (x^{2} ln (\frac{1}{x}))

Simplify

x^{2} ln (\frac{1}{x}) : - x^{2} ln (x)

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

Simplify

- (2 x ln (x) + \frac{1}{x} x^{2}) : - 2 x ln (x) - x

= - 2 x ln (x) - x

What is the derivative of x^2ln(1/x) ?
The derivative of x^2ln(1/x) is -2xln(x)-x
What is the first derivative of x^2ln(1/x) ?
The first derivative of x^2ln(1/x) is -2xln(x)-x