Find the Derivative of the function y = (2 - 2b) tanh^-1 b?

[KAISER91]

Homework Statement

Find the Derivative of the function y = (2 - 2b) tanh^-1 b?

Homework Equations

The Attempt at a Solution

The answer given is [2 / (1 + b)] - 2 tanh^-1 b

I've tried this question several times to no avail.

I used the product rule with u = (2 - 2b) and v = tanh^-1 b

What am I doing wrong?

y' = (2 -2b) (1/ 1- b^2) + (tanh^-1) (-2)

 

[micromass]

I see the (2 -2b) (1/ 1- b^2) part. But how did you arrive at tanh^{-1}(-2)??

Also note that since 1-b^2=(1+b)(1-b). So,

\frac{2-2b}{1-b^2} = \frac{2}{1+b}

and this is indeed the first term of the solution.

 

[KAISER91]

(tanh^-1 b) (-2)

I forgot the b.

(tanh^-1 b) is v and -2 is simply the derivative of (2-2b)

so that is -2 tanh^-1 b which is the second part.Thanks for your help.