Differentiating Inverse Trig Functions

# Differentiating Inverse Trig Functions - Differentiating...

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Differentiating Inverse Trig Functions

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Getting the inverse of a function. Swap the and and rewrite in terms of y Inverse functions ARE FUNCTIONS They must pass the vertical line test
Inverse functions must pass the vertical line test But since inverse functions are reflections of the original function in the line The original function should pass the HORIZONTAL line test

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fails the horizontal line test (but we want to talk about inverse trig functions) So we “cheat” and only use from The domain is The range is
This is the graph of The domain and the range have swapped around

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Same deal with only Note domain and range

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Rules for differentiating inverse trig functions
Remember If you are given the function Then And it works the other way around too Can be written

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If we have And we want we turn the expression round We know how to differentiate this WRT because we can differentiate implicitly Woo!
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