the derivitive of function?

Question

cot to power-1 * [(cos2x) to power 1/2 ] at x=pi/6

Answer 1

If this is what you mean:{(cot x)^-1}*{sqrt(cos 2x)}

then answer is:

Let y={(cot x)^-1}*{sqrt(cos 2x)}
=>dy/dx=[{(cot x)*[1/2cos(2x)]*[-sin(2x)]*2} - {sqrt(cos 2x) *
-(cosec x)^2}]/(cot(x))^2

Answer 2

the derivative=[-1/(1+cos^2(2x)]
*[(-2sin2x)]
=-4rt3/5

Answer 3

gopal forgot the chain rule