Chapter A6, Problem 30E

To determine

To find: the derivative of y

Answer to Problem 30E

The derivative of y is $\frac{dy}{dt}=1-2t{\coth }^{-1}t$

Explanation of Solution

Given:

  $y=\left(1-t^2\right){\coth }^{-1}t$

Calculation:

Given $y=\left(1-t^2\right){\coth }^{-1}t$

To find $\frac{dy}{dt},$ differentiate $y$ with respect to $t$

  $\Rightarrow \frac{dy}{dt}=\left(1-t^2\right)\left[\frac{1}{1-t^2}\right]+(-2t){\coth }^{-1}t$

  $\frac{dy}{dt}=1-2t{\coth }^{-1}t$

Conclusion:

Therefore, The derivative of y is $\frac{dy}{dt}=1-2t{\coth }^{-1}t$