Chapter 2 - Derivatives - 2.9 Linear Approximations and Differentials - 2.9 Exercises - Page 193: 16

(a) The derivative of $$ y=\cos \pi x $$ is $$ d y=-\pi \sin( \pi x) d x $$ (b) When $$ x=1 / 3 \,\,\,\ \text{and} \,\,\,\,\, d x=-0.02$$, $$ d y=-\pi \sin( \frac{\pi}{3} ) (-0.02)=0.02\pi \frac{\sqrt{3}}{2}$$

(a) The derivative of $$ y=\cos \pi x $$ is $$ d y=-\pi \sin( \pi x) d x $$ (b) When $$ x=1 / 3 \,\,\,\ \text{and} \,\,\,\,\, d x=-0.02$$, $$ d y=-\pi \sin( \frac{\pi}{3} ) (-0.02)=0.02\pi \frac{\sqrt{3}}{2}$$