What is the derivative of #f(x)=cos^-1(x)# ?
Here's how we obtain this common derivative:
Differentiate both sides of
This will entail using Implicit Differentiation on the right side:
We need to get rid of the
We previously said
Now, recall the identity
In the identity, replace
#f(x)=cos^-1(x)" "=>" "cos(f(x))=x#
Take the derivative of both sides. Use the chain rule on the left.
The last step came from the identity
Note about domain: the domain of