find the derivative of cotx by the first principle?

let f(x)  = cot xd f(x) dx  = limh0f(x+h)-f(x)h =limh0cot (x+h)-cot xh =limh01hcos(x+h)sin(x+h)- cos(x)sin(x) =limh01hsin(x)cos(x+h)-sin(x+h)cos(x)sin(x+h)sin(x) =limh01hsin(x - x - h)sin(x+h)sin(x) =limh01hsin(- h)sin(x+h)sin(x) =limh0-sin(h)hlimh01sin(x+h)sin(x)  = (-1)1sin2 x = -cosec2 x    .......Ans

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