How do you find the derivative of y=arc cot(x)?

1 Answer
Dec 3, 2016

dy/dx = -1/(1+x^2)

Explanation:

When tackling the derivative of inverse trig functions. I prefer to rearrange and use Implicit differentiation as I always get the inverse derivatives muddled up, and this way I do not need to remember the inverse derivatives. If you can remember the inverse derivatives then you can use the chain rule.

Let y=arc cot(x) <=> coty=x

Differentiate Implicitly:

-csc^2ydy/dx = 1 ..... [1]

Using the csc"/"cot identity;

1+cot^2y=csc^2y
:. 1+x^2=csc^2y
:. csc^2y=1+x^2

Substituting into [1]
:. -(1+x^2)dy/dx=1
:. dy/dx = -1/(1+x^2)