What is the ((log_{10}(x))/x)^' ?

The ((log_{10}(x))/x)^' is (1-ln(x))/(ln(10)x^2)

What is the first ((log_{10}(x))/x)^' ?

The first ((log_{10}(x))/x)^' is (1-ln(x))/(ln(10)x^2)

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(\frac{lo g _{10} ( x )}{x})^{^{'}}

\frac{1 - ln ( x )}{ln ( 10 ) x ^{2}}

Solution steps

(\frac{lo g _{10} ( x )}{x})^{'}

Apply the Quotient Rule:

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

= \frac{( lo g _{10} ( x ) ) ^{^{'}} x - x ^{^{'}} lo g _{10} ( x )}{x ^{2}}

(lo g_{10} (x))^{'} = \frac{1}{x ln ( 10 )}

x^{'} = 1

= \frac{\frac{1}{x l n ( 10 )} x - 1 \cdot lo g _{10} ( x )}{x ^{2}}

Simplify

\frac{\frac{1}{x l n ( 10 )} x - 1 \cdot lo g _{10} ( x )}{x ^{2}} : \frac{1 - ln ( x )}{ln ( 10 ) x ^{2}}

= \frac{1 - ln ( x )}{ln ( 10 ) x ^{2}}

What is the ((log_{10}(x))/x)^' ?
The ((log_{10}(x))/x)^' is (1-ln(x))/(ln(10)x^2)
What is the first ((log_{10}(x))/x)^' ?
The first ((log_{10}(x))/x)^' is (1-ln(x))/(ln(10)x^2)