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Calculus - Coggle Diagram
Calculus
Derivative formulas through geometry
Safe to ignore
''Power rule''
Essence of calculus
Circle
It gets better for smaller
dr
Break area of the circle into rings
Area under the graph
Hard problem
Sum of many small values
Area under a graph
dr
Gives the spacing between different values of R
''Integral'' of x^2
Gets better as
dx
approaches 0
''Derivative'' of A
Fundamental theorem of calculus
Chain rule and product rule
Sum rule
Product rule
''Left d(Right) + Right d(Left)''
Function composition
Chain rule
Another way to visualize derivatives
f(x) as a transformation
Measures stretch/squishing
The paradox of the derivative
What is a derivative?
Instantaneous rate of change?
Change
Requires multiple points in time
Instantaneous
One point in time
Paradoxes
At time t=0, is the car moving?
Best constant approximation
Derivative
dt
is not ''infinitely small''
dt
is not 0
Best constant approximation around a point
Using ''d'' announces that
dt
approaches 0
