Differentiating Inverse Hyperbolic Functions

[lmw1891]

Hey. I have this homework problem. y=xtanh[sup:e11vg11x]-1[/sup:e11vg11x]2x. I need to derive it. I'm not too sure on how to get started. Can anyone help please?

 

[BigGlenntheHeavy]

\(\displaystyle y \ = \ uv\)

\(\displaystyle y' \ = \ u'v \ + \ uv'\)

\(\displaystyle Now, \ all \ you \ need \ to \ know \ is \ D_x[tanh^{-1}(2x)], \ assuming \ you \ know \ D_x[x].\)

 

[galactus]

A handy little identity that may help in differentiating this is:

\(\displaystyle tanh^{-1}(2x)=\frac{ln(2x+1)}{2}-\frac{ln(1-2x)}{2}\)