Chapter 6 - Applications of Integration - 6.8 Logarithmic and Exponential - 6.8 Exercises - Page 480: 34

$$f'\left( x \right) = \pi {x^{\pi - 1}}$$

$$\eqalign{ & f\left( x \right) = {x^\pi } \cr & {\text{evaluate the derivative}} \cr & f'\left( x \right) = \frac{d}{{dx}}\left( {{x^\pi }} \right) \cr & {\text{general power rule}} \cr & \frac{d}{{dx}}\left( {{x^p}} \right) = p{x^{p - 1}},{\text{ }}p = \pi \cr & then \cr & f'\left( x \right) = \pi {x^{\pi - 1}} \cr} $$