Can anyone help me find the derivative of the following function:

f(x) = ( x + cot(x/2))

d/dx [x + cot(x/2)]
d/dx [x] + d/dx [cot(x/2)]
1 - csc²(x/2) d/dx [x/2]
1 - (1/2)csc²(x/2)

That, like most trig stuff, comes in many different equivalent forms, but this is the most direct derivative.

Deriv of x = 1

Deriv of cot(u) = -csc^(u)*du/dx

The deriv of x/2 is 1/2.

Putting that all together, we have

f'(x) = 1 - csc^2(x/2)*1/2

= 1 - (1/2)csc^2(x/2)

Jen

f(x) = ( x + cot(x/2))

df/dx = -1/2 cos(x) csc^2 (x/2)