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
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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
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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
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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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