Find derivative of cot(2x+1) using first principle of derivative

Find derivative of cot(2x+1) using first principle of derivative 6. Find derivative of cot + l) using first principle of derivative.

Dear student,

Let f(x)=cot(2x+1)Then f(x+h)=cot[2(x+h)+1]=cot(2x+2h+1)df(x)dx=limh0f(x+h)-f(x)h=limh0cot(2x+2h+1)-cot(2x+1)h=limh0cos(2x+2h+1)sin(2x+2h+1)-cos(2x+1)sin(2x+1)h=limh0sin(2x+1).cos(2x+2h+1)-cos(2x+1).sin(2x+2h+1)h.sin(2x+1).sin(2x+2h+1)=limh0sin(2x+1-(2x+2h+1))h.sin(2x+1).sin(2x+2h+1)     [As sin(A-B)=sinA. cosB-cosA.sinB]=limh0sin(-2h)h.sin(2x+1).sin(2x+2h+1)=-limh02.sin(2h)2h.sin(2x+1).sin(2x+2h+1)=-limh0sin2h2h.limh01sin(2x+1).sin(2x+2h+1)=-2×1×1sin(2x+1)sin(2x+1)=-2sin2(2x+1)=-2cosec2(2x+1)

Regards,

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