Prove that (d)/(dx) (ln |x|)=1/x, x != 0

Siemensueqw

Siemensueqw

Answered question

2022-11-09

Prove that d d x ( ln | x | ) = 1 x ,   x 0

Answer & Explanation

erlent00s

erlent00s

Beginner2022-11-10Added 15 answers

Here we have to prove d d x ( ln | x | ) = 1 x ,   x 0
By exponential and logarithmic functions
As we know that d d x ( e x ) = e x
Let us take y = ln x
This can be written as
e y = x
differentiating it wrt x we have
d d x ( e y ) = d d x ( x ) e y d y d x = 1 d y d x = 1 e y d y d x = 1 e ln x e | n e x = x d y d x = 1 x d d x | n x = 1 x

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