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

The derivative of x^nln(1/x) is -nx^{n-1}ln(x)-x^{n-1}

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

The first derivative of x^nln(1/x) is -nx^{n-1}ln(x)-x^{n-1}

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

- n x^{n - 1} ln (x) - x^{n - 1}

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= - n x^{n - 1} ln (x) - x^{n - 1}

\frac{- 3}{( s - 2 ) ^{2}}

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

\int tan (5 x) d x

\frac{d}{d x} (\frac{x ^{2} - 2 x + 5}{x ^{2} + 9})

\int (- \frac{3}{10 - 10 x ^{2}}) d x

What is the derivative of x^nln(1/x) ?
The derivative of x^nln(1/x) is -nx^{n-1}ln(x)-x^{n-1}
What is the first derivative of x^nln(1/x) ?
The first derivative of x^nln(1/x) is -nx^{n-1}ln(x)-x^{n-1}