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# ws16 - the domains of the derivatives a y =[ln(cos x e...

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WORKSHEET 16 - Fall 1995 1. Compute dy dx for the following. a) y = (arccos x )(cos x ) b) y = arccos(cos x ) c) y 4 x 7 = 8 d) y = sin 3 x 2 + 1 x 2 e) y = arctan x tan x 2. Suppose θ = arcsin x with 1 x 1. Find the following in terms of x : cos θ tan θ cot θ sec θ csc θ sin( θ ) . 3. Redefine arcsin x to give the angle θ [ π 2 , 3 π 2 ] such that sin θ = x and rework problem 2. 4. a) Let f ( x ) = arcsin x + arccos x . Give two separate arguments to show that f is a constant. What is that constant? b) Lef f ( x ) = arcsin(cos x ) for 0 x π . Show that f ( x ) = ax + b for constants a and b . Find them. 5. Compute the derivatives of the following functions. What are the domains of the functions? What are
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Unformatted text preview: the domains of the derivatives? a) y = [ln(cos x )] e arcsin x b) y = ln r x + 1 x − 1 ! c) y = x x 2 6. a) Using the identity sin(2 y ) = 2 sin y cos y , show that 2 arcsin x = arcsin(2 x p 1 − x 2 ) . ( ∗ ) Hint: Let y = arcsin x . b) Plug in x = 1 into ( ∗ ). c) For what values of x is ( ∗ ) valid? Why?...
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