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Unformatted text preview: Math 116  Lab 3  Fall 2011.
Rules for diﬀerentiation, chain rule, derivatives of trig, exponential, hyperbolic, inverse
trig and inverse hyperbolic functions (Sections 3.3, 3.53.7 of L/G).
You are to provide full solutions to the following problems. You are allowed to collaborate with your
classmates, use your notes and textbook and ask the TA for guidance. Direct copying of solutions
is not encouraged, nor is it allowed or ethical. First name: Last name:
Student number: 1 Math 116  Lab 3  Fall 2011. Student number: Rules for diﬀerentiation, chain rule, derivatives of trig, exponential, hyperbolic, inverse trig
and inverse hyperbolic functions (Sections 3.3, 3.53.7 of L/G). 1. Determine the equation of the tangent line to the graph of f at the speciﬁed value of
x0 . Show all steps.
x 1
2 a) f (x) = , x0 = 4 b) f (x) = sin(5x), x0 =
2. Show that d
dt π
4 cosh(ωt) = ω sinh(ωt). Show all steps. 3. Product Rule: Use the product rule to determine a formula for f (x). Show all steps.
a) f (x) = tan(2x) tan(7x).
b) f (x) = x4 e5x sin(3x).
4. Quotient Rule: Use the quotient rule to determine a formula for f (x). Show all steps.
a) f (x) =
b) f (x) = cos(2x)
.
x3 −5x+2
√
x
cot(x) . 5. Chain Rule: Use the chain rule as well as other techniques for diﬀerentiation to
determine a formula for f (x). Show all steps.
a) f (x) = tan2 (7x) − sec2 (7x).
b) f (x) = cot 3−14x3
9+x4 . c) f (x) = secn (x).
d) Let g (x) = sin(x), h(x) = 3x8 − 2x + 1 and deﬁne f (x) = h(g (x)).
6. Find the derivative of the following functions. Show all steps.
a) f (t) = tan−1 (e−3t ).
b) f (t) = cos−1 (t)
.
sin−1 (t) c) f (t) = ecot −1 (t) . d) f (t) = log4 (t cos(t)).
e) f (t) = ln 4(2t−1)2
1−9t . 2 ...
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 Spring '11
 RobertAndre
 Calculus, Chain Rule, Derivative, Hyperbolic Functions, TA

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