What is the derivative of log_{10}(1/x) ?

The derivative of log_{10}(1/x) is -1/(xln(10))

What is the first derivative of log_{10}(1/x) ?

The first derivative of log_{10}(1/x) is -1/(xln(10))

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derivative of

lo g_{10} (\frac{1}{x})

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

Solution steps

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

Simplify

lo g_{10} (\frac{1}{x}) : - lo g_{10} (x)

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the derivative log rule:

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

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

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