Difference between revisions of "Introduction to Calculus: What is Derivative and Integral"

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This is a topic ties every things about (functions and graphs) together.  
This is a topic ties everything about (functions and graphs) together.  


We're mainly concerned with two parts:
We're mainly concerned with two parts:
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#Integrals (Integration)
#Integrals (Integration)


Derivative is equal to rate of change. Most of the time we will us <math> dy \over dx </math> to present how one variable changes with another.  
A derivative is equal to the rate of change. Most of the time we will use <math> dy \over dx </math> to present how one variable changes with another.  
The derivative is the gradient of a tangent line  
The derivative is the gradient of a tangent line.


But from the beginning we are going to talk about where do you want the derivative, the other way to say is I will give you a point and then tell me what's the derivative or gradient for that point.
But from the beginning, we are going to talk about where do you want the derivative, the other way to say is I will give you a point and then tell me what's the derivative or gradient for that point.


From the beginning here is the concepts you need for calculus.
From the beginning here are the concepts you need for calculus.
#"what is the derivative at x=n" you can under stand as "what is the gradient when x=n"
#"what is the derivative at x=n" you can understand as "what is the gradient when x=n".
#"What is the Integral at x=a to x=b" you can under stand as  "what is the area between the function and the x axis from x=a to x=b".
#"What is the integral at x=a to x=b" you can understand as  "what is the area between the function and the x-axis from x=a to x=b".


Conclusion (from the beginning )
Conclusion (from the beginning )


derivative = gradient of a tangent = rate of change
derivative = gradient of a tangent = rate of change.
 
Integral = area under the function.
Integral = area under the function.
 
<noinclude>
==examples==
==examples==
#what is the derivative at x=5
#What is the derivative at x=5
#what is the derivative at x=9
#What is the derivative at x=9
#what is the derivative at x=2
#What is the derivative at x=2
#What is the integral from x=1 to x=4
#What is the integral from x=3 to x=10
#What is the integral from x=6 to x=10 - by the Integral from x=7 to x=10
[[File:Screen Shot 2021-08-24 at 9.09.34 PM.png|thumb]]
</noinclude>

Latest revision as of 12:55, 24 September 2021

This is a topic ties everything about (functions and graphs) together.

We're mainly concerned with two parts:

  1. Derivative (Differentiation)
  2. Integrals (Integration)

A derivative is equal to the rate of change. Most of the time we will use to present how one variable changes with another. The derivative is the gradient of a tangent line.

But from the beginning, we are going to talk about where do you want the derivative, the other way to say is I will give you a point and then tell me what's the derivative or gradient for that point.

From the beginning here are the concepts you need for calculus.

  1. "what is the derivative at x=n" you can understand as "what is the gradient when x=n".
  2. "What is the integral at x=a to x=b" you can understand as "what is the area between the function and the x-axis from x=a to x=b".

Conclusion (from the beginning )

derivative = gradient of a tangent = rate of change.

Integral = area under the function.

examples

  1. What is the derivative at x=5
  2. What is the derivative at x=9
  3. What is the derivative at x=2
  4. What is the integral from x=1 to x=4
  5. What is the integral from x=3 to x=10
  6. What is the integral from x=6 to x=10 - by the Integral from x=7 to x=10
Screen Shot 2021-08-24 at 9.09.34 PM.png
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