Introduction to Calculus: What is Derivative and Integral

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 $dy \over dx$ 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