Derivative of ln(sinx) by First Principle

Formula to find derivative of a function f(x) by first principle :

This is also called as limit definition of the derivative.

Derivative of ln(sinx) using first principle :

Let f(x) = ln(sinx).

When h ---> 0, cosh ---> 1

From standard results of limits,

Let t = cotxsinh.

When h = 0,

t = cotx[sin(0)]

t = (cotx)(0)

t = 0

Therefore, when h ---> 0, t ---> 0

From standard results of limits,

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