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Popular >

derivative of (ln(u))/u

Solution

derivative of

\frac{ln ( u )}{u}

Solution

\frac{1 - ln ( u )}{u ^{2}}

Solution steps

\frac{d}{d u} (\frac{ln ( u )}{u})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d u}{d u} = 1

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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