Chapter A6, Problem 14E

To determine

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

Answer to Problem 14E

The derivative of y is $\frac{dy}{dx}=\cosh (2x+1)$ .

Explanation of Solution

Given:

  $y=\frac{1}{2}\sinh (2x+1)$

Calculation:

The given entity

  $y=\frac{1}{2}\sinh (2x+1)$

Now, differentiating y with respect to x,

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

Conclusion:

Therefore, the derivative of y is $\frac{dy}{dx}=\cosh (2x+1)$ .