How do you differentiate log_2(x)?

Olszarv5h

Olszarv5h

Answered question

2023-02-12

How to differentiate log 2 ( x ) ?

Answer & Explanation

Peso6gn

Peso6gn

Beginner2023-02-13Added 7 answers

Step 1
As a result of the general formula:
XXX d d x ( log a ( x ) ) = 1 x ln ( a )
Giana Jensen

Giana Jensen

Beginner2023-02-14Added 1 answers

Step 1
As we know how to differentiate ln ( x ) , we should change the base of the logarithm first.
The according formula to change a logarithmic expression from the base a to the base b is
log a ( x ) = log b ( x ) log b ( a )
The formula is as follows:
log 2 ( x ) = ln ( x ) ln ( 2 )
As 1 ln ( 2 ) is just a constant and the derivative of ln ( x ) is 1 x , our derivative is:
d d x [ log 2 ( x ) ] = d d x [ ln ( x ) ln ( 2 ) ] = 1 ln ( 2 ) 1 x = 1 x ln ( 2 )

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