Equations in Slope-Intercept

1. (10 pts each) Find the derivatives of the following functions (a-c): Do not simplify your ans a.
f(x)=sec(tan(x
4
+e
4
))
b.
g(x)=ln(
csc(x)

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e
2
+e
4x


)
c.
h(x)= Equations in Slope-Intercept
5
sin(x)

x
3
+cos(x)

2. (15 pts) Find
y

and the two equations of the tangent line to the graph of
x
3
+3xy
2
+y=15
when
x=1
. (Use exact values and write the equations in slope-intercept form) 3. ( 10 pts) Find
f

and the equation of the tangent line to
f(x)=
x

e
x

at the point where
x=4
. (Use exact values and write the equations in slope-intercept form) 4. (15
pts)
Find
dx
dy

and the equation of the tangent ine on the curve parametrized by
{
x(t)=t
2
+1
y(t)=t
2
−t Equations in Slope-Intercept

where the tangent line has slope

2
1

. (Use exact values and write the equations in slopeintercept form) Equations in Slope-Intercept

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