Answer :
Let f(x) = cosec x cot x
By product rule
f’(x) = cosec x (cot x)’ + cot x (cosec x)’ ……..(1)
Let f1(x) = cot x, accordingly f1(x + h) = cot (x + h)
By first principle
=
= 
=
= 
= 
∴ (cot x)’ = - cosec2 x ………………..(2)
Let f2(x) = cosec x, accordingly f2(x + h) = cosec (x + h)
By first principle
=
=
= 
= 
= 
= -cosec x cot x
∴ (cosec x)’ = -cosec x cot x ……………….(3)
Putting the value of (2) and (3) in (1)
f’(x) = cosec x (-cosec2 x) + cot x (-cosec x cot x)
= - cosec3 x – cot2 x cosec x
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
view all courses
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
