# Thread: Derivation and Integration Numerical

1. ## Derivation and Integration Numerical

Consider a signal function of time in the form:
$t=0:0.005:10$
$y=(2sin(2 \pi t)exp(-0.1t)+0.2cos(20 \pi t)) / (4-0.1t+0.2sin(10 \pi t))$

How to derive two times the signal y?

2. If your code is MATLAB source, Please type:

>> syms t
>> y=(2*sin(2*pi*t)*exp(-0.1*t)+0.2*cos(20 *pi* t)) / (4-0.1*t+0.2*sin(10 *pi *t))
>> diff(y, 2)

3. Originally Posted by math2009
If your code is MATLAB source, Please type:

>> syms t
>> y=(2*sin(2*pi*t)*exp(-0.1*t)+0.2*cos(20 *pi* t)) / (4-0.1*t+0.2*sin(10 *pi *t))
>> diff(y, 2)
I need to know how to calculate by hand

4. I guess I have to get a polynomial interpolation and derive this polynomial.
How can I get the polynomial interpolation of this function?

5. I found the 1st derivative:

y | 0 | 0.005 | 10
f(t) | 0.05 | 0.0503 | 0.2271

Newton interpolation:

$F[x_0 , x_1] = \frac{f(x_1)-f(x_0)}{x_1 - x_0} = 0.06$

$F[x_0,x_1,x_2] = -4.231x10^{-3}$

$p(x) = f(x_0)+(x-x_0)F[x_0,x_1]+(x-x_0)(x-x_1)F[x_0,x_1,x_2]$
$p(x) = -4.231x10^{-3}x^2 + 0.06021x + 0.05$

$f'(t) = p'(x)$
$f'(t) = 8.462x10^{-3}x + 0.06021$

Is correct ?
For the second derivative I need to interpolate again?

6. I have an observation in this exercise that I did not understand.
OBS: Use 0.005s step to derive