100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Maths Formulas and notes R80,00   Add to cart
Quickly navigate to
Preview
  2.  
  3. Stellenbosch University (SUN)
  4.  
  5. Mathematics 144

Class notes

Maths Formulas and notes
 34 views  1 purchase

List of all Derivative Formula, Integral Formula, Notes On how to do Trig Substitution, integration by parts, Partial Fractions, Trig Graphs, Inverse Graphs, Logarithmic Derivations and Exponential Derivations

Preview 2 out of 9  pages

Document information

  • August 18, 2022
  • 9
  • 2022/2023
  • Class notes
  • Dr wessels
  • Integrals, derivatives, partials frcrions, trig substitution

Subjects

Written for

All documents for this subject (7)

Seller

avatar-seller
catherinedent

Content preview

Trig Identities
𝑠𝑖𝑛(𝑥)
tan(x) = 𝑐𝑜𝑠(𝑥)
1
cosec(x) = 𝑠𝑖𝑛(𝑥)
𝑠𝑖𝑛 → 𝑐𝑜𝑠𝑒𝑐
1
sec(x) = 𝑐𝑜𝑠(𝑥)
𝑐𝑜𝑠 → 𝑠𝑒𝑐
1 𝑐𝑜𝑠(𝑥)
cot(x) = 𝑡𝑎𝑛(𝑥)
= 𝑠𝑖𝑛(𝑥) 𝑡𝑎𝑛 → 𝑐𝑜𝑡


Identity Rules
2 2
𝑠𝑖𝑛 (𝑥) + 𝑐𝑜𝑠 (𝑥) = 1
2 2
⇒ 1 − 𝑠𝑖𝑛 (𝑥) = 𝑐𝑜𝑠 (𝑥)
2 2
⇒ 1 − 𝑐𝑜𝑠 (𝑥) = 𝑠𝑖𝑛 (𝑥)
2 2
𝑡𝑎𝑛 (𝑥) + 1 = 𝑠𝑒𝑐 (𝑥)
2 2
⇒ 𝑡𝑎𝑛 (𝑥) = 𝑠𝑒𝑐 (𝑥) − 1
2 2
𝑐𝑜𝑡 (𝑥) + 1 = 𝑐𝑜𝑠𝑒𝑐 (𝑥)
Complementary Angles:
𝑠𝑖𝑛θ = 𝑐𝑜𝑠(90 − θ)
𝑐𝑜𝑠θ = 𝑠𝑖𝑛(90 − θ)
𝑡𝑎𝑛θ = 𝑐𝑜𝑡(90 − θ)
Compound Angles:
𝑠𝑖𝑛(α + β) = 𝑠𝑖𝑛α 𝑐𝑜𝑠β + 𝑐𝑜𝑠α 𝑠𝑖𝑛β
𝑠𝑖𝑛(α − β) = 𝑠𝑖𝑛α 𝑐𝑜𝑠β − 𝑐𝑜𝑠α 𝑠𝑖𝑛β
𝑐𝑜𝑠(α + β) = 𝑐𝑜𝑠α 𝑐𝑜𝑠β − 𝑠𝑖𝑛α 𝑠𝑖𝑛β
𝑐𝑜𝑠(α − β) = 𝑐𝑜𝑠α 𝑐𝑜𝑠β + 𝑠𝑖𝑛α 𝑠𝑖𝑛β
𝑡𝑎𝑛α + 𝑡𝑎𝑛β
𝑡𝑎𝑛(α + β) = 1− 𝑡𝑎𝑛α 𝑡𝑎𝑛β
𝑡𝑎𝑛α − 𝑡𝑎𝑛β
𝑡𝑎𝑛(α − β) = 1+ 𝑡𝑎𝑛α 𝑡𝑎𝑛β

Double Angles:
2𝑡𝑎𝑛𝑥
𝑠𝑖𝑛(2𝑥) = 2 𝑠𝑖𝑛𝑥 𝑐𝑜𝑠 𝑥 = 2
1+𝑡𝑎𝑛 𝑥
2 2
𝑐𝑜𝑠(2𝑥) = 𝑐𝑜𝑠 𝑥 − 𝑠𝑖𝑛 𝑥
2
= 2 𝑐𝑜𝑠 𝑥 − 1
2
= 1 − 2 𝑠𝑖𝑛 𝑥
2𝑡𝑎𝑛𝑥
𝑡𝑎𝑛(2𝑥) = 2
1−𝑡𝑎𝑛 𝑥
2
𝑐𝑜𝑡 𝑥−1
𝑐𝑜𝑡(2𝑥) = 2𝑐𝑜𝑡𝑥

, 𝑑
Constant Rule 𝑑𝑥
c=0
𝑑 𝑛 𝑛−1
Power Rule 𝑑𝑥
𝑥 = 𝑛. 𝑥
𝑑
Sum Rule 𝑑𝑥
f(x) + g(x) = f’(x) + g’(x)
𝑑
Difference Rule 𝑑𝑥
f(x) - g(x) = f’(x) - g’(x)
𝑑
Product Rule 𝑑𝑥
(f(x) . g(x))= f’(x).g(x) + f(x).g’(x)
𝑑 𝑓’(𝑥).𝑔(𝑥) − 𝑓(𝑥).𝑔’(𝑥)
Quotient Rule 𝑑𝑥
(f(x) . g(x))= 2
[𝑔(𝑥)]
𝑑
Chain Rule 𝑑𝑥
(f(g(x)) = f’(g(x).g’(x)
𝑑 𝑥 𝑥
Exponential Rule 𝑑𝑥
𝑏 = 𝑏 ln(b)
𝑑 1
Logarithmic Rule 𝑑𝑥
ln(x) = 𝑥


Log Rule Derivatives
𝑑 1
𝑑𝑥
ln(x) = 𝑥
,x>0
𝑑 𝑔'(𝑥)
𝑑𝑥
ln(g(x)) = 𝑔(𝑥)
𝑑 1
𝑑𝑥
𝑙𝑜𝑔𝑎x = 𝑥 𝑙𝑛 𝑎
, x>0
𝑑 𝑔'(𝑥)
𝑑𝑥
𝑙𝑜𝑔𝑎g(x) = 𝑔(𝑥) 𝑙𝑛 𝑎


Exponential Function Derivatives
𝑑 𝑥 𝑥
𝑑𝑥
(𝑒 ) = 𝑒
𝑑 𝑥 𝑥
𝑑𝑥
(𝑎 ) = 𝑎 ln 𝑎
𝑑 𝑔(𝑥) 𝑔(𝑥)
𝑑𝑥
(𝑒 )=𝑒 g ‘ (x)
𝑑 𝑔(𝑥) 𝑔(𝑥)
𝑑𝑥
(𝑎 ) = 𝑙𝑛(𝑎) 𝑎 g ‘(x)

Trigonometric Derivatives
𝑑
𝑑𝑥
sin(x) = cos(x)
𝑑
𝑑𝑥
cos(x) = -sin(x)
𝑑
𝑑𝑥
tan(x) = sec2(x)
𝑑
𝑑𝑥
cosec(x) = - cosec(x) cot(x)
𝑑
𝑑𝑥
sec(x) = sec(x) tan(x)
𝑑
𝑑𝑥
cot(x) = -cosec2(x)

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying this summary from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller catherinedent. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy this summary for R80,00. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

76449 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy summaries for 14 years now

Start selling
R80,00  1x  sold
  • (0)
  Buy now