Derivatives of Trigonometric Functions

Question

Find the equation of the line that is tangent to the curve y = 2xcosx at the point (π,−2π).

The equation of this tangent line can be written in the form y = mx + b where

m =

b =

Answer 1

y=2xcos(x)

y'(x)=-2xsin(x)+2cos(x)

m = y'(π) = 0+2(-1) = -2 at (π, -2π)

y(π) = -2π

y - (-2π) = -2(x-π)

y = -2x+2π-2π

y = -2x