Chapter 2 - Derivatives - 2.9 Linear Approximations and Differentials - 2.9 Exercises - Page 193: 15

(a) The derivative of $$ y=\tan x $$ is $$ d y=\sec ^{2} x d x $$ (b) When $$ x=\pi / 4 \,\,\,\ \text{and} \,\,\,\,\, d x=-0.1$$, $$ dy=[\sec (\pi / 4)]^{2}(-0.1)=(\sqrt{2})^{2}(-0.1)=-0.2$$

(a) The derivative of $$ y=\tan x $$ is $$ d y=\sec ^{2} x d x $$ (b) When $$ x=\pi / 4 \,\,\,\ \text{and} \,\,\,\,\, d x=-0.1$$, $$ dy=[\sec (\pi / 4)]^{2}(-0.1)=(\sqrt{2})^{2}(-0.1)=-0.2$$