What is the derivative of (log_{10}(x)/x) ?

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

What is the first derivative of (log_{10}(x)/x) ?

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

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\frac{d}{d x} (\frac{lo g _{10} ( x )}{x})

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

Solution steps

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

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

\frac{d x}{d 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}}

n = 0 \sum \infty \frac{1}{0. 5 ^{n}}

(12 - 6 y + e^{- 3 x}) d x - 2 d y = 0

\int \frac{x ^{3}}{x ^{4} + 10} d x

(sin^{3} (t))^{^{'}}

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