Derivative of x·tanh⁻¹x + ln√(1-x²)

[neosonata]

Homework Statement

Find the derivative. Simplify where possible.

xtanh^-1x + ln$\sqrt{1-x^2}$

Homework Equations

The Attempt at a Solution

(x/1+x²) + tanh^-1x - (x/1-x²)How would I go about make this problem simplified as possible if the above answer is correct.

 

[tiny-tim]

welcome to pf!

hi neosonata! welcome to pf!

(x/1+x²)

nooo …

that's for tan^-1x ​

 

[Simon Bridge]

I think that first term is not correct - can you check?
I have $$\frac{d}{dx}\tanh^{-1}(x)=\frac{1}{1-x^2}$$
http://en.wikipedia.org/wiki/Hyperbolic_function#Derivatives

 

[litup]

hi neosonata! welcome to pf!


nooo …

that's for tan^-1x ​

He must have written it wrong since that would just be X^3.

 

[neosonata]

Ah that make sense.. silly me :p

it should be

(x/1-x^2) + tanh^(-1)x - (x/1-x^2)

which leaves

tanh^(-1)x

Thanks for the help guys