Web resources available

This quiz tests the work covered in Lecture 16 and corresponds to Section 3.5 of the textbook Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et al.).
There are more web quizzes at Wiley, select Section 5.

Section 3.7 of The Mathematics Learning Centre’s booklet on differentiation Introduction to Differential Calculus covers differentiating trigonometric functions.

http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/derivative/trig2.html gives another explanation of the derivative of the basic trigonometric functions.

There is an applet at http://www.ies.co.jp/math/java/calc/sin_diff/sin_diff.html which graphs the derivatives by looking at the tangent to the curve.

You might want to go back to http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/chainruledirectory/ChainRule.html or http://archives.math.utk.edu/visual.calculus/2/chain_ rule.2/ and try the trigonometrical problems if you haven’t already.

Question 1

a)		If   then
b)		If   then
c)		If   then
d)		If   then
e)		If   then

 

There is at least one mistake.
For example, choice (a) should be true.

There is at least one mistake.
For example, choice (b) should be false.

If   then 

There is at least one mistake.
For example, choice (c) should be false.

If   then 

There is at least one mistake.
For example, choice (d) should be true.

There is at least one mistake.
For example, choice (e) should be false.

If   then 

Your answers are correct

1. True.
2. False. If   then 
3. False. If   then 
4. True.
5. False. If   then 

Question 2

a)				b)
c)				d)

 

Not correct. Choice (a) is false.

Try again, you have not applied the chain rule correctly.

Not correct. Choice (b) is false.

Try again, you have not applied the chain rule correctly.

Your answer is correct.

Not correct. Choice (d) is false.

Try again, watch the sign.

Question 3

a)				b)
c)				d)

 

Your answer is correct.

Not correct. Choice (b) is false.

Try again, you have not used the chain rule correctly for the second term.

Not correct. Choice (c) is false.

Try again, you have successfully found the derivative of  

Not correct. Choice (d) is false.

Try again, you have seem to be trying to find the derivative of  

Question 4

a)
b)
c)
d)		None of the above.

 

Not correct. Choice (a) is false.

Try again, you have not differentiated the first term correctly, you may have a sign problem as well.

Not correct. Choice (b) is false.

Try again, you have not differentiated the first term correctly.

Not correct. Choice (c) is false.

Try again, you have not differentiated the second term correctly.

Your answer is correct.