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Reciprocal Derivatives: Inverse Functions Insights

Discover the derivative of an inverse function and apply it to one-to-one functions in various examples. Learn the reciprocal rule for derivatives and find the derivative of inverse trigonometric functions. Practice problems from the textbook included.

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Reciprocal Derivatives: Inverse Functions Insights

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  1. 5.3 The Derivative of an Inverse Function

  2. Remember… • If a function f has an inverse function f-1, Then f (a) = b implies that f-1(b) = a. • x’s and y’s switch!

  3. The Derivative of f -1(x):So…The derivative of the inverse is the reciprocal of the derivative of the original

  4. Ex 1) Given that y = f(x) = x3 + 2x – 3 is a one-to–one function, and thus has an inverse, find (f-1)'(0).

  5. Ex 2) • Find , if: & .

  6. 5.6 The Derivative of Inverse Trig Functions

  7. Ex 3) Find y:

  8. Ex 4) Find y:

  9. Ex 5) Find y:

  10. HW – 5.3 pg. 349# 71 – 75 odds, 95 5.6 pg. 378# 41 – 49 odds, 61 & 63

  11. Ex 1) Let g be the function which converts from Fahrenheit to Celsius. Then g (F) = C = (5/9) (F – 32) Find g-1:

  12. Ex 3) • Find , if: , , & .

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