hw10-7 - Math 170-010 Homework 10/7 Fall 2011 Goals:...

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Homework 10/7 Fall 2011 Goals: Compute derivatives of inverse trig functions using implicit diFerentiation. Use “quick” rules for inverse sine and tangent problems. Exercises: 1. This exercise is uses implicit diFerentiation to compute the derivative of y = cos 1 x , also known as y = arccos x . (a) Start with y = arccos x . Apply cos to both sides. (b) You now have cos y = x . ±ind y using implicit diFerentiation. (c) Think of y as the angle in the triangle below, so that cos y = x 1 = adjacent hypotenuse y 1 x Compute the length of the side opposite y . You should get a formula involving x . (d) Compute sin y . Then substitute this in your answer from part (b). 2. Repeat this technique to compute the derivative of y = tan 1 x , also known as arctan x . (a) Start with y = arctan x . Apply tan to both sides. (b) ±ind y using implicit diFerentiation. (c) Think of
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hw10-7 - Math 170-010 Homework 10/7 Fall 2011 Goals:...

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