5-6 and 5-7 Derivatives and Integrals of Inverse Trig Functions

5-6 and 5-7 Derivatives and Integrals of Inverse Trig Functions

5-6 Derivatives of Inverse Trig Functions Rizzi Calc BC

Previously On Concept of and relationship between y=sinx and y=arcsinx Graph of y=sinx and y=arcsinx Proof of Derivative

Lets take the derivative of Start by letting Now You Try Try taking the derivative of

But what happens when What if the inside isnt just x? Lets try it with Can we come up with a formalized rule for the

derivative in words and in a formula? Now You Try Try it with Write the rule in words and in a formula

Practice Problems Do the following practice problems from the book: 5.6 #39, 43, 59, 61 5-7 Integrals of

Inverse Trig Functions Rizzi Calc BC

Lets Work Backwards Using our rules for derivatives and knowledge of u-substitutions, lets try to work backwards to integrate the following.

First, identify whether its arcsin or arctan Together What about this one?

Try These 1+( +3)2 2 1

And One More This one requires some fancy simplifying first:

Practice Problems Do the following practice problems from the book: 5.7 #1, 7, 9, 27, 43

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