9pt 1. Di↵erentiate each function:
(a) f (x) = (x2 + 3x) cos(2x)
p
(b) h(x) = arcsin( x).
dy
8pt 2. Given y = (sin x)1/x , use logarithmic di↵erentiation to find .
dx
, 12pt 3. Consider the equation tan(x2 + y) = xy 3 + 1.
dy
(a) Use implicit di↵erentiation to find .
dx
(b) Find an equation of the tangent line to the graph of tan(x2 + y) = xy 3 + 1 at the point
(1, 1).
(a) f (x) = (x2 + 3x) cos(2x)
p
(b) h(x) = arcsin( x).
dy
8pt 2. Given y = (sin x)1/x , use logarithmic di↵erentiation to find .
dx
, 12pt 3. Consider the equation tan(x2 + y) = xy 3 + 1.
dy
(a) Use implicit di↵erentiation to find .
dx
(b) Find an equation of the tangent line to the graph of tan(x2 + y) = xy 3 + 1 at the point
(1, 1).
