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Chapter 2: Q 39. (page 237)

Fill in the blank:

ddx(tanh-1x)=___________.

Short Answer

Expert verified

ddx(tanh-1x)=11-x2.

Step by step solution

01

Given Information  

The given expression is ddx(tanh-1x).

02

Simplification  

We know that,

tanh-1x=12{lnx+1-ln1-x}.

we compute the derivative of ddx(tanh-1x).

We get,

ddx(tanh-1x)=ddx[12{lnx+1-ln1-x}=12{1(x+1).1-1(1-x).-1}=12(1x+1+11-x)=12.2(1-x2)=11-x2Therefore,ddx(tanh-1x)=11-x2.

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