Find an equation of the tangent line to the curve at the given point.

Question

y = 4e^xcos(x), (0, 4)

Answer 1

dy/dx = 4 [ e^x (-sin x) + cos x (e^x) ]
at x = 0
dy/dx = m = 4 [ 0 + 1 ] = 4
so
y = 4 x + b
at x = 0, y = 4
4 = 4(0) + b so b = 4
y = 4 x + 4