If f (x) is the integral function of the function 2sin⁡x−sin⁡2xx3,x≠0, then limx→0 f′(x) is equal to

Since  f (x) is the integral function of 2sin⁡x−sin⁡2xx3∴f′(x)=2sin⁡x−sin⁡2xx3Now,limx→0 f′(x)=limx→0 2sin⁡x−sin⁡2xx3⇒ limx→0 f′(x)=limx→0 2sin⁡xx×1−cos⁡xx2⇒ limx→0 f′(x)=2limx→0 sin⁡xx×limx→0 1−cos⁡xx2=2×12=1.