The utility of derivative

A major feature in calculus is “change”.
We require to know how a thing is changing another one so.. we could say “the relationship between two things is a function“. As we wiggle the input point of a function we can know how the output is changing.
But a question is still open What is the ratio which is changing the output value?
Well such ratio is the derivative.

slope_ecuation

#include <stdio.h>
#include <stdint.h>

#define __MAX_X_VALUE  20

static int f_x(int x)
{
   return 6*x - 9;
}

int main(void)
{
    for(int a = 0; a < __MAX_X_VALUE ;a++)
    {
       printf("f(%d)= 6(%d)-9 = %d\n", a, a, f_x(a));
    }
}
optimus@house:~$ g++ slope_ecuation.cpp ; ./a.out
f(0)= 6(0)-9 = -9
f(1)= 6(1)-9 = -3
f(2)= 6(2)-9 = 3
f(3)= 6(3)-9 = 9
f(4)= 6(4)-9 = 15
f(5)= 6(5)-9 = 21
f(6)= 6(6)-9 = 27
f(7)= 6(7)-9 = 33
f(8)= 6(8)-9 = 39
f(9)= 6(9)-9 = 45
f(10)= 6(10)-9 = 51
f(11)= 6(11)-9 = 57
f(12)= 6(12)-9 = 63
f(13)= 6(13)-9 = 69
f(14)= 6(14)-9 = 75
f(15)= 6(15)-9 = 81
f(16)= 6(16)-9 = 87
f(17)= 6(17)-9 = 93
f(18)= 6(18)-9 = 99
f(19)= 6(19)-9 = 105

What is impedance for AC circuits ?

Impedance of a circuit: It is the total effect of resistance or the measure of opposition to the passage of the current and its unit is the ohm. The term impedance is represented with the use of letter Z.

Impedance for resistors, capacitors and inductors have to be calculated slightly different. Due to current/voltage behavior for each one. As you can see pretty denoted at the image below:

* Resistors remains unaffected the frequency of current/voltage.
* Capacitor leads voltage by 90 degrees ahead.
* Capacitor lags voltage by 90 degrees earlier.

impidance

How to calculate Z for resistors in AC circuit ?
In this specific case there is not much to do. Because the value of R is remained as a constant. (It is perhaps an obvious matter as per the fact that resistors do not affect any frequency).

How to calculate Z for capacitors (AKA capacitive reactance) in AC circuit ?
First of all. To understand how the following calculation works, it is required the concept of radian in wikipedia. Afterward It’ll be comprehend.

Zc = 1/(w*c) = 1/(2pi*f*c)
w = radian frequency in rad/s = 2pi*f*c
where f is the frequency in hertz of the voltage source.
c = capacitance in farads.

How to calculate Z for inductors (AKA inductive reactance) in AC circuit ?

Zl =  2pi*f*l
l = inductance in henries.