1.

Find derivatives using the first principle, cosecx

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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


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