We want to find 
/
/
du
du dx
dv
=dv dx Clearly
du
dx  = 2 sin x cos x and dv
dx  = e cos x (– sin x) = – (sin x) e cos x
Thus
du
dv  =
cos
cos
2sin
cos
2cos
sin
x
x
x
x
x
x e
= −e
−
Miscellaneous Exercise on Chapter 5
Differentiate w r t