Question

find the derivative of
y= xsinx+ cos x??

Answer 1

find the derivative of sin and cos, the derivative table can be found here http://tutorial.math.lamar.edu/Classes/CalcI/DiffTrigFcns.aspx

Answer 2

dy/dx = cos(x) - sin(x)

dy/dx = 0.

0 = cos(x) - sin(x)

sin(x) = cos(x)

sin(x)/cos(x) = 1
tan(x) = 1
x = (pi/4 + k*pi | k an integer )

If x = pi/4, then
y = sin(pi/4) + cos(pi/4)
= sqrt(2)/2 + sqrt(2)/2
= 2sqrt(2)/2
= sqrt(2)

If x = 5pi/4, then
y = sin(5pi/4) + cos(5pi/4)
y = -sqrt(2)/2 + -sqrt(2)/2
y = -sqrt(2)

The maximum of these two values is sqrt(2), so that is the maximum value.-Puggy YH