Chapter 6 - Applications of Integration - 6.10 Hyperbolic Functions - 6.10 Exercises - Page 503: 22

$$\frac{{dy}}{{dx}} = 4\cosh 4x$$

$$\eqalign{ & y = \sinh 4x \cr & {\text{computing }}dy/dx \cr & \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left( {\sinh 4x} \right) \cr & {\text{by the chain rule}} \cr & \frac{{dy}}{{dx}} = \cosh 4x\frac{d}{{dx}}\left( {4x} \right) \cr & \frac{{dy}}{{dx}} = \cosh 4x\left( 4 \right) \cr & {\text{multiplying}} \cr & \frac{{dy}}{{dx}} = 4\cosh 4x \cr} $$