# Chapter 4 - Calculating the Derivative - Chapter Review - Review Exercises - Page 244: 32

$$\frac{{dy}}{{dx}} = 4{e^{0.5x}}$$

#### Work Step by Step

\eqalign{ & y = 8{e^{0.5x}} \cr & {\text{differentiate both sides}} \cr & \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {8{e^{0.5x}}} \right] \cr & \frac{{dy}}{{dx}} = 8\frac{d}{{dx}}\left[ {{e^{0.5x}}} \right] \cr & \frac{{dy}}{{dx}} = 8\left( {0.5{e^{0.5x}}} \right) \cr & \frac{{dy}}{{dx}} = 4{e^{0.5x}} \cr}

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