What is the derivative of log_{10}(2-x) ?

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

What is the first derivative of log_{10}(2-x) ?

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

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derivative of

lo g_{10} (2 - x)

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

Solution steps

\frac{d}{d x} (lo g_{10} (2 - x))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

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

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{2 - x} \frac{d}{d x} (2 - x)

= \frac{1}{2 - x} \frac{d}{d x} (2 - x)

\frac{d}{d x} (2 - x) = - 1

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

Simplify

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

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

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