Summary
Summary Calculus Basics Notes 2024 Latest
- Course
- Institution
Calculus Basics Notes
[Show more]
1 review
By: Bruce5759wayne • 3 months ago
Seller
Follow
APlusAchiever
Reviews received
Content preview
Calculus Basics Notes1. Derivative:
The derivative measures the rate of change of a function at a given point. It represents the
slope of the tangent line to the function's graph at that point. Mathematically, the derivative of a
function f(x) is denoted as f'(x) or dy/dx and is defined as:
f'(x) = lim(h→0) [f(x + h) - f(x)] / h
2. Integral:
The integral is used to compute the accumulation of a quantity over an interval. It
represents the area under the curve of a function. The definite integral of a function f(x) over an
interval [a, b] is denoted as ∫[a, b] f(x) dx and is defined as:
∫[a, b] f(x) dx = lim(n→∞) Σ[f(x_i)Δx]
where x_i are the partition points of the interval [a, b], Δx represents the width of each
subinterval, and the sum is taken over all the subintervals.
3. Chain Rule:
The chain rule is used to differentiate composite functions. It enables the differentiation
of a function within a function. Mathematically, if y = f(g(x)), the chain rule states:
This study source was downloaded by 100000888273843 from coursesidekick.com on 07-16-2024 09:07:16 GMT -05:00
https://www.coursesidekick.com/mathematics/4179650
, dy/dx = dy/du * du/dx
where u = g(x) and f'(u) represents the derivative of f with respect to u.
4. Product Rule:
The product rule allows the differentiation of a product of two functions. Mathematically,
if y = f(x) * g(x), the product rule states:
d(fg)/dx = f'(x) * g(x) + f(x) * g'(x)
where f'(x) and g'(x) represent the derivatives of f(x) and g(x), respectively.
5. Quotient Rule:
The quotient rule enables the differentiation of a quotient of two functions.
Mathematically, if y = f(x) / g(x), the quotient rule states:
d(f/g)/dx = [f'(x) * g(x) - f(x) * g'(x)] / [g(x)]^2
where f'(x) and g'(x) represent the derivatives of f(x) and g(x), respectively.
6. Fundamental Theorem of Calculus:
This study source was downloaded by 100000888273843 from coursesidekick.com on 07-16-2024 09:07:16 GMT -05:00
https://www.coursesidekick.com/mathematics/4179650
The benefits of buying summaries with Stuvia:
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
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
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 these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller APlusAchiever. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.89. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
53068 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now