Chapter 2 - Derivatives - 2.4 Derivatives of Trigonometric Functions - 2.4 Exercises - Page 150: 22

$y=x+1$

Given: $y=(1+x) \cos x$ Apply product rule, we get $y'=\cos x-(1+x) \sin x$ At $(0, 1)$, we have $y'=\cos(0)-(1+0) \sin (0)=1$ so we have $m=y'=1$ Formula to tangent line is : $y=mx+b$ $y-y_1=m(x-x_1)$ At $(0, 1)$, we have $y-1=1(x-0)$ This implies $y=x+1$