Question

Find derivatives using the first principle, cosecx

Answer 1

Answer is :

We have to find the derivative of cosec x using first Principle

Solution :

From the definition of the cosecant function we know that,

csc x=1 / sinx

From Derivative of Sine Function:

d/ dx(sinx)= cosx

Now,using chain rule:

d/ dx(cscx) = cosx−1 / sin2x (Chain Rule for Derivatives)

= −1/ sinx * cosx / sinx

= −coscx . cotx

Answer

The derivative of cosec x is −cosx .cotx