further calculus (1 Viewer)

[Pote]

this is a very easy question, but i still need help -.-

can anyone show me how to show:

d [tan^-1 (cot x)] / dx = -1

i just learnt this, and my concepts still aren't that clear. thanks for your help!

 

[icycloud]

y = arctan(cot(x))

Let u = cot(x)
du = -csc²(x) dx

Now y = arctan(u)
dy = du / (1 + u²)
= -csc²(x) dx / (1 + cot²(x))

Thus, dy/dx = -csc²(x)/csc²(x)
= -1 #