How do you find the derivative of cot x?

We need to find the derivative of cot x

Solution

We can find the derivative of cot x by the following method

We know that

cotx=cosx / sinx

We now use the quotient rule of differentiation way to find the derivative of cot x

d/ dx cotx=d / dx(cosx / sinx) {Quotient rule: d / dx(uv)=( vdu / dx−udv / dx) / v2}

= (d / dxcosx)sinx−cosx(d/ dxsinx) / sin2x————-(i)

Using the formulae for the derivative of the trigonometric functions sinx and cosx given by

d/dx cosx=−sinx and d/dx sinx=cosx

Substituting the above values in equation (i) we get

d/ dx cotx=−sinx sinx−cosx cosx / sin2x

= sin2x+cos2x / sin2x

= −1/sin2x

=−csc2x

d/ dx cotx =−csc2x

Answer

Derivative of cot x is −csc2x

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