Question

How do you find the derivative of `(tanx)^-1`?

Answer 1

I would rewrite the function before differentiating

Explanation:

`(tanx)^-1 = 1/tanx = cotx`

Now use the memorized `d/dx(cotx) = -csc^2x` or rewrite another step

`cotx = cosx/sinx` and use the quotient rule to get

`d/dx(cotx) = (-sin^2x-cos^2x)/sin^2x = (-1)/sin^2x = -csc^2x`