What is the derivative of x^{-1}ln(x) ?

The derivative of x^{-1}ln(x) is (-ln(x)+1)/(x^2)

What is the first derivative of x^{-1}ln(x) ?

The first derivative of x^{-1}ln(x) is (-ln(x)+1)/(x^2)

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{- 1}, g = ln (x)

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

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

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

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

Simplify

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

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

y^{^{'}} = y (x y^{4} + 4)

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

\frac{d}{d x} (6 sin^{2} (x))

\frac{d}{d t} (π t^{2})

\int 16 - r^{2} r d r

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