Question

HELP !
g(x) = arctanh (log x)

Solve for g'(x) and find values for x for which g'(x) is defined .

Answer 1

thats easy

Answer 2

\[\frac{d}{dx} \tanh^{-1} (x) = \frac{1}{1-x^2}\]

Answer 3

u= ln(x)
du/dx= (1/x)

Answer 4

by chain rules \[\frac{d}{dx} \tanh^{-1} (\ln(x) ) = \frac{1}{1-(\ln(x))^2} \times \frac{1}{x}\]

Answer 5

so the derivative is not defined when the denominator is zero

Answer 6

so when x=0 , or when 1-[ln(x)]^2 =0

Answer 7

ln(x) = +- 1

so not defined when \[x=0, \frac{1}{e} , e \]

Answer 8

thanks ! you're awesome ! :D