Derivative of Inverse Trig Functions via Implicit Differentiation

Description:
Implicit Differentiation let's us solve a whole class of derivatives we haven't been able to do yet. In this video we look at arctan(x), the inverse function to tan(x). Using implicit differentiation we can compute the derivative of this function!
Learning Objectives:
1) Compute the derivative of inverse trig functions (an other inverse functions too)
Now it's your turn:
1) Summarize the big idea of this video in your own words
2) Write down anything you are unsure about to think about later
3) What questions for the future do you have? Where are we going with this content?
4) Can you come up with your own sample test problem on this material? Solve it!
Learning mathematics is best done by actually DOING mathematics. A video like this can only ever be a starting point. I might show you the basic ideas, definitions, formulas, and examples, but to truly master calculus means that you have to spend time - a lot of time! - sitting down and trying problems yourself, asking questions, and thinking about mathematics. So before you go on to the next video, pause and go THINK.
This video is part of a Calculus course taught by Dr. Trefor Bazett at the University of Cincinnati.
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[@kylenason]

I was wondering, do you have a video on derivatives of inverse functions?

[@DrTrefor]

Not specifically, but it is almost identical to what was done here. Take the derivative for both sides of the composition of the function and its inverse.

[@mohammadfallahzade2110]

You explain these concepts very well Thank you

[@standowner6979]

I really enjoyed this lecture