Chapter A6, Problem 17E

To determine

To find: the derivative of the given equation of y with respect to appropriate variable.

Answer to Problem 17E

The derivative is $\frac{dy}{dz}=\coth z$ .

Explanation of Solution

Given:

  $y=\ln (sinhz)$

Calculation:

The derivative of y with respect to z is calculated below

  $y=\ln (sinhz)$

Differentiating y with respect to z

  $\begin{array}{l}\frac{dy}{dz}=\frac{\cosh z}{\sinh z}\\ \frac{dy}{dz}=\coth z\end{array}$

Conclusion:

Therefore, the derivative is $\frac{dy}{dz}=\coth z$ .