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Popular >

derivative of 1/x ln(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = \frac{1}{x}, g = ln (x)

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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