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Understanding Derivatives of Inverse Functions

Learn how to find derivatives of inverse functions using implicit differentiation and the Chain Rule. Discover the relationship between trigonometric functions and inverse trigonometric functions. Practice with examples using calculus techniques.

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Understanding Derivatives of Inverse Functions

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  1. 3.8 Derivatives of Inverse Functions

  2. But recall that has a range of… implies that… Look this up if you don’t remember… over the domain Really, look this up if you don’t remember…

  3. But so is positive. Use implicit differentiation to find: in terms of x only And since we know that siny = x Remember? Trig?

  4. We could use the same technique to find and . d - 1 sec x dx Try a few angles to confirm this.

  5. We could use the same technique to find and . d - 1 sec x dx This is how the book expresses them, the difference here being… The Chain Rule

  6. Your calculator contains all six inverse trig functions. However it is occasionally still useful to know the following: p

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