Chapter A6, Problem 13E

To determine

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

Answer to Problem 13E

The derivative of y is $\frac{dy}{dx}=2\cosh \frac{x}{3}$ .

Explanation of Solution

Given:

  $y=6\sinh \frac{x}{3}$

Calculation:

The given entitiy

  $y=6\sinh \frac{x}{3}$

Now, differentiating y with respect to x,

  $\begin{array}{l}\frac{dy}{dx}=6\cosh \frac{x}{3}(\frac{1}{3})\\ \frac{dy}{dx}=2\cosh \frac{x}{3}\end{array}$

Conclusion:

Therefore, the derivative of y is $\frac{dy}{dx}=2\cosh \frac{x}{3}$ .