What is the derivative of 1/cotx?

Question

do i change it to tanx or divide 1 by derivative of cotx?

Answer 1

1/cotx= tanx

d(tanx)/dx =  sec^2X  answer

Answer 2

1/cotx = tanx = sinx/cosx

Integrate sinx/cosx dx

u = cosx

du/dx = sinx

du=sinxdx

now integrate 1/u du

= ln|u| + C

plug u back in

= ln|cosx| + C

Answer 3

Yes change it to tan(x) and then differentiate.

Answer 4

You can do it either way.

y=tan(x)

dy/dx = sec^2(x) --- answer

Directly:

y= 1/cot(x) = cot(x)^(-1)

dy/dx = (-1)cot(x)^(-2) (-csc^2(x))

dy/dx = csc^2(x) / cot^2(x)

=[1/sin^2(x)][ sin^2(x) /cos^2(x)]

= 1/cos^2(x) = sec^2(x)