What is the ((ln(x))/x)^' ?

The ((ln(x))/x)^' is (1-ln(x))/(x^2)

What is the first ((ln(x))/x)^' ?

The first ((ln(x))/x)^' is (1-ln(x))/(x^2)

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(\frac{ln ( x )}{x})^{^{'}}

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

Solution steps

(\frac{ln ( x )}{x})^{'}

Apply the Quotient Rule:

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

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

(ln (x))^{'} = \frac{1}{x}

x^{'} = 1

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

Simplify

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

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

x \to + 4 lim (x - 2)

\int_{0}^{π} (x cos (2 x)) d x

\frac{d y}{d t} - 0.1 y = - t

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

\frac{1}{sin ^{2} ( x )}