What is the derivative of (log_{2}(x)/x) ?

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

What is the first derivative of (log_{2}(x)/x) ?

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

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\frac{d}{d x} (\frac{lo g _{2} ( x )}{x})

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

Solution steps

\frac{d}{d x} (\frac{lo g _{2} ( x )}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( lo g _{2} ( x ) ) x - \frac{d x}{d x} lo g _{2} ( x )}{x ^{2}}

\frac{d}{d x} (lo g_{2} (x)) = \frac{1}{x ln ( 2 )}

\frac{d x}{d x} = 1

= \frac{\frac{1}{x l n ( 2 )} x - 1 \cdot lo g _{2} ( x )}{x ^{2}}

Simplify

\frac{\frac{1}{x l n ( 2 )} x - 1 \cdot lo g _{2} ( x )}{x ^{2}} : \frac{1 - ln ( x )}{ln ( 2 ) x ^{2}}

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

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