Question

Cot 3x+1 by first principle

Answer 1

Answer:

-3cosec²(3x+1)

Step-by-step explanation:

Differentiation from the first principle is that the function Cot(3x + 1)

is differentiable at a point x if the limit

lim           ( f(x+h) - f(x) ) / h

h->0                                  

exists

cot(3x + 1 + h) - cot(3x + 1) / h

(cos(3x + 1 + h)/sin(3x +1 +h)) - (cos(3x +1) / sin(3x+1)) / h

cos(3x + 1 + h)sin(3x+1) - cos(3x +1)sin(3x +1 +h) / (sin(3x+1+h)sin(3x+1)(h))

3sin(3x+1 - (3x+1+h) ) / sin(3x+1+h)sin(3x+1)(h)

-3sin(h) / (h)sin(3x+1+h)sin(3x+1)

now we know that (sinh / h) = 1  and h = 0

-3/ sin(3x+1+0)sin(3x+1)

-3 / sin(3x+1)sin(3x+1)

-3 / sin²(3x+1)

-3cosec²(3x+1)