Difference between revisions of "Introduction to Calculus: What is Derivative and Integral"
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This is a topic ties | 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: | ||
| Line 5: | Line 5: | ||
#Integrals (Integration) | #Integrals (Integration) | ||
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 | From the beginning here are the concepts you need for calculus. | ||
#"what is the derivative at x=n" you can | #"what is the derivative at x=n" you can understand as "what is the gradient when x=n". | ||
#"What is the | #"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 | #What is the integral from x=1 to x=4 | ||
#What is the | #What is the integral from x=3 to x=10 | ||
#What is the | #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:
- Derivative (Differentiation)
- 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.
- "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 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
- What is the derivative at x=5
- What is the derivative at x=9
- 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
