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40833_2Mastering_Derivatives.pdf http://www.CrystalClearMaths.com © Graeme Henderson (2015) ~ Free Use Permitted ~ Page 1 ~ Calculus The art of measuring
shape and variation!Practice worksheets for
Mastery of Differentiation
Graeme Henderson
http://www.CrystalClearMaths.com © Graeme Henderson (2015) ~ Free Use Permitted ~ Page 2 ~Dear Reader,
It is no secret that, to master any skill, we need to practise it!School textbooks usually contain sufficient material for you to learn HOW to use certain skills but,
This publication is intended to fill that gap !
If you are a student, let me suggest that you set time aside regularly to work through a few examples
from this booklet. It need not be a great deal of time, but I recommend that, on a weekly, fortnightly, or monthly basis, you spend a few minutes practising the art of finding derivatives.You may find it a useful exercise to do this with friends and to discuss the more difficult examples.
To parent check your answers. If you are a teacher, please note that the sheets have been designed so that they may be laminated back-to-back (questions on one side and answers on the other) and used in a classroom setting.I have invested a great deal of time in putting this material together. Although I have tried to be
very careful, it is quite likely that some mistakes appear in the answers. If you find any, please let
me know by visiting my Crystal Clear Mathematics website and leaving a message on the Contact age. If you give permission for me to mention you by name, I will acknowledge your contribution in future (corrected) editions. Because this took so long to prepare (dozens of hours), and because I am making it available for free, it would be appreciated if you could consider making a donation towards the upkeep of my maintain the site and add videos and other resources. Any contribution you may be able to make in return for the free use of this material would be greatly appreciated.I hope this booklet is of help to you!
Graeme Henderson
B.Sc. (Hons), B.Th. (Hons),
Dip.Ed., Dip.Min.
16 April 2015
Copyright
Although I holds the copyright on all the material that I Mastery of Differentiationbooklet),everything that I produce is available for FREE DOWNLOAD worldwide as long as no commercial gain is made from
it. I am determined that people from poorer families and from developing nations have free access to quality training
materials in mathematics.If you can afford to support this ministry, any donation that you can make via the website will be gratefully received.
Speaking of copyright, thank you, Schristia (on Flickr), for allowing me to use your image for the cover of this booklet.
http://www.CrystalClearMaths.com © Graeme Henderson (2015) ~ Free Use Permitted ~ Page 3 ~ Derivatives in Your Head! Differentiate with respect to x: A B C D E F G1. x3 4x3 ͺݔଶ
͵ ݔ
ଵ ଶ ͵ݔ ଵ ଷ xq+2 ξݔ2. x10 8x െݔଶ
- ݔ ଷ ସ Ͷݔ ଷ ସ x3m ξݔఱ3. x4 5x4 ͷݔଷ
Ͷ ݔ
ଶ ଷ െݔ ଶ ଷ xp+q െඥݔଶళ4. x5 -3x2 -ݔହ
͵ ݔ
ହ ସ െͳ-ݔିଷ ହ -x171 ඥݔଷర5. x6 2x െݔ
ݔ
ଷ ଶ ͻݔ ଶ ଷ xn+1 ඥݔ଼య6. x2 8 -
ͻݔଷ x1.8 ͳͶݔିଷ
xm+n+1 െඥݔଵǤ଼7. x7 -7x6 ͳͳ
ͷݔହ x6.1 െ-ݔିସ
ହ -x5d-k+6 ඥݔଶǤସయ8. x9 9x5 െ͵
Ͷݔ x3.4 Ͷݔିହ
ଷ ݔξଶାଵ ඥݔିହǤଵయ9. x -12x7 ͵
ݔସ ݔିଵ
ଶ െݔ ଶ ଷ ݔଷగାସ ඨͳݔǤ
10. x0 -14 ͷ
ͺݔଷ ݔି
ଶ Ͷݔ ହ ସͷ ݔଷିଶ െͳ
ξݔଷర
11. x-2 -8x0 െݔିଷ
͵ ݔିସ
ଷ െ-͵ݔ
ଷ ଶ ߨξݔଶఱ
12. x-1 11x-7 -ݔି
ͻ ݔିହ
ସ Ͷ -ͳݔ ଶ -5x2n+1 െඨͳݔଶ
య13. x-4 9x-8 െͶݔିହ
ͳͷ x-5.3 െͻ
Ͷݔିସ
ଷ 3x5k+4 ͳξݔଷ
14. x-3 -14x-10 ͷݔିଵସ
x-2.6 െ-ݔ
ହ ସ ͷ െͶݔξଷା ݔξݔ15. x-10 4x-3 െ-
ͻݔିଷ x-8.3 Ͷ
͵ݔ
ଷ ξ͵ݔగିଶ െͷ͵ξݔ
16. x-7 5x-1 ͳ
ͷݔିଷ ݔ
ଵଵ ହ -ݔିଶ
ହ -2ݔହାଵ ඨͳݔିଵǤଶ
ర17. x-16 -2x-6 െͺ
ͷݔିସ ݔ
ହ െͻݔି଼ ହͶ 2.5x2e+3 െ͵
ξݔଵǤସ
18. x-9 3x-5 Ͷ
ݔି ݔିଽ
ଶ െ͵ͳͶݔ
ଷ 0.4x6f ͳͶ͵ξݔଷళ
19. x-6 -7x-4 ͷ
ͺݔଷ -7x-4 ͳ-
ͻݔିଷ
ହ 2xa+b ݔଶξݔయ20. x-11 6x-2 െͷ
ͳͶݔି 6x-2 ݔିହ ଷ - 3.5x4w+2 െ-ݔଷξݔఱ
http://www.CrystalClearMaths.com © Graeme Henderson (2015) ~ Free Use Permitted ~ Page 4 ~Derivatives in Your Head (Answers)! Solutions:
A B C D E F G1. 3x2 12x2 ͳݔ
͵ ݔିଵ
ଶ - ݔିଶ ଷ (q+2)xq+1 ݔିଵ ଶ -ൌͳ -ξݔ2. 10x9 8 െݔ ͵ݔିଵ
ସͶ ͵ݔିଵ
ସ 3mx3m-1 ݔିସ ହͷൌͳ
ͷξݔସఱ
3. 4x3 20x3 ͳͷݔଶ
Ͷ -ݔିଵ
ଷ͵ െͶݔିଵ
ଷ (p+q)xp+q-1 െ-ݔିହ ൌെ-
ξݔହళ
4. 5x4 -6x ͳ-ݔସ
͵ ͷݔ
ଵ ସͶ ݔି଼
ହ -171x170 ͵ݔିଵ ସͶൌ͵
Ͷξݔర
5. 6x5 2 െݔ ͵ݔ
ଵ ଶ - ݔିଵ ଷ (n+1)xn ͺݔ ହ ଷ͵ൌͺξݔହయ
͵6. 2x 0 -
͵ݔଶ 1.8x0.8 െݔିଵ (m+n+1)xm+n െ-ǤͻݔିǤଵ7. 7x6 -42x5 ͳͳݔସ 6.1x5.1 ͺݔିଽ
ହ ͷ -(5d-k+6)x5d-k+5 -ǤͺݔିǤଶ8. 9x8 45x4 െͻ
-ݔହ 3.4x2.4 െ--ݔି଼ ଷ͵ ሺξ-ͳሻݔξଶାଵ െͳǤݔିଶǤ