Worksheet 2.6 - The Chain Rule Worksheet With Answers - Calculus Maximus Page 4
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7Calculus Maximus
WS 2.6: Chain Rule
( )
2
2
=
+
7. Find the derivative of
f x
sin
x
cos
x
two different ways,
(a) By using the chain rule on the given expression.
(b) By using and identity first, then differentiating.
(c) What’s the moral of THIS story? (Hint: It is NOT “Flattery is a dangerous weapon in the hands of
the enemy.”)
( )
( )
( )
( )
=
2
=
2
′
′
=
8. Using calculus and trig Identities, prove that if
f x
tan
x
and
g x
sec
x
, then
f x
g x
.
9. Using the chain rule,
( )
( )
−
= −
(a) Prove that the derivative of an odd function is an even function. That is if
, then
f
x
f x
( )
( )
′
′
−
=
.
f
x
f x
(b) What type of function do you think the derivative of an even function is? Justify in a manner
similar to part (a).
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