/x - 1\ log|-----| \x + 1/
log((x - 1)/(x + 1))
Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
Apply the quotient rule, which is:
and .
To find :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
To find :
Differentiate term by term:
The derivative of the constant is zero.
Apply the power rule: goes to
The result is:
Now plug in to the quotient rule:
The result of the chain rule is:
Now simplify:
The answer is:
/ 1 x - 1 \ (x + 1)*|----- - --------| |x + 1 2| \ (x + 1) / -------------------------- x - 1
/ -1 + x\ / 1 1 \ |-1 + ------|*|----- + ------| \ 1 + x / \1 + x -1 + x/ ------------------------------ -1 + x
/ -1 + x\ / 1 1 1 \ 2*|-1 + ------|*|- -------- - --------- - ----------------| \ 1 + x / | 2 2 (1 + x)*(-1 + x)| \ (1 + x) (-1 + x) / ----------------------------------------------------------- -1 + x