How can I find first and second derivative?

excelos

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Hello,

How can I graph and find the first and second derivative of a graph?

Thanks!
 

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Numerically (first-order divided differences),

[Table="width:, class:grid"][tr][td="bgcolor:#C0C0C0"][/td][td="bgcolor:#C0C0C0"]
A​
[/td][td="bgcolor:#C0C0C0"]
B​
[/td][td="bgcolor:#C0C0C0"]
C​
[/td][td="bgcolor:#C0C0C0"]
D​
[/td][td="bgcolor:#C0C0C0"]
E​
[/td][td="bgcolor:#C0C0C0"]
F​
[/td][/tr][tr][td="bgcolor:#C0C0C0"]
1​
[/td][td="bgcolor:#F3F3F3"]
x
[/td][td="bgcolor:#F3F3F3"]
y
[/td][td="bgcolor:#F3F3F3"]
dy/dx
[/td][td="bgcolor:#F3F3F3"]
d2y/dx
[/td][td="bgcolor:#F3F3F3"]
[/td][td="bgcolor:#F3F3F3"]
[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
2​
[/td][td]
0​
[/td][td]
0.000​
[/td][td][/td][td][/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
3​
[/td][td]
1​
[/td][td]
0.309​
[/td][td="bgcolor:#CCFFCC"]
0.309​
[/td][td][/td][td][/td][td="bgcolor:#CCFFCC"]C3: =(B3 - B2)/($A3 - $A2)[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
4​
[/td][td]
2​
[/td][td]
0.588​
[/td][td="bgcolor:#CCFFCC"]
0.279​
[/td][td="bgcolor:#CCFFFF"]
-0.030​
[/td][td][/td][td="bgcolor:#CCFFFF"]D4: =(C4 - C3)/($A4 - $A3)[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
5​
[/td][td]
3​
[/td][td]
0.809​
[/td][td="bgcolor:#CCFFCC"]
0.221​
[/td][td="bgcolor:#CCFFFF"]
-0.058​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
6​
[/td][td]
4​
[/td][td]
0.951​
[/td][td="bgcolor:#CCFFCC"]
0.142​
[/td][td="bgcolor:#CCFFFF"]
-0.079​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
7​
[/td][td]
5​
[/td][td]
1.000​
[/td][td="bgcolor:#CCFFCC"]
0.049​
[/td][td="bgcolor:#CCFFFF"]
-0.093​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
8​
[/td][td]
6​
[/td][td]
0.951​
[/td][td="bgcolor:#CCFFCC"]
-0.049​
[/td][td="bgcolor:#CCFFFF"]
-0.098​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
9​
[/td][td]
7​
[/td][td]
0.809​
[/td][td="bgcolor:#CCFFCC"]
-0.142​
[/td][td="bgcolor:#CCFFFF"]
-0.093​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
10​
[/td][td]
8​
[/td][td]
0.588​
[/td][td="bgcolor:#CCFFCC"]
-0.221​
[/td][td="bgcolor:#CCFFFF"]
-0.079​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
11​
[/td][td]
9​
[/td][td]
0.309​
[/td][td="bgcolor:#CCFFCC"]
-0.279​
[/td][td="bgcolor:#CCFFFF"]
-0.058​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
12​
[/td][td]
10​
[/td][td]
0.000​
[/td][td="bgcolor:#CCFFCC"]
-0.309​
[/td][td="bgcolor:#CCFFFF"]
-0.030​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
13​
[/td][td]
11​
[/td][td]
-0.309​
[/td][td="bgcolor:#CCFFCC"]
-0.309​
[/td][td="bgcolor:#CCFFFF"]
0.000​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
14​
[/td][td]
12​
[/td][td]
-0.588​
[/td][td="bgcolor:#CCFFCC"]
-0.279​
[/td][td="bgcolor:#CCFFFF"]
0.030​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
15​
[/td][td]
13​
[/td][td]
-0.809​
[/td][td="bgcolor:#CCFFCC"]
-0.221​
[/td][td="bgcolor:#CCFFFF"]
0.058​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
16​
[/td][td]
14​
[/td][td]
-0.951​
[/td][td="bgcolor:#CCFFCC"]
-0.142​
[/td][td="bgcolor:#CCFFFF"]
0.079​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
17​
[/td][td]
15​
[/td][td]
-1.000​
[/td][td="bgcolor:#CCFFCC"]
-0.049​
[/td][td="bgcolor:#CCFFFF"]
0.093​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
18​
[/td][td]
16​
[/td][td]
-0.951​
[/td][td="bgcolor:#CCFFCC"]
0.049​
[/td][td="bgcolor:#CCFFFF"]
0.098​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
19​
[/td][td]
17​
[/td][td]
-0.809​
[/td][td="bgcolor:#CCFFCC"]
0.142​
[/td][td="bgcolor:#CCFFFF"]
0.093​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
20​
[/td][td]
18​
[/td][td]
-0.588​
[/td][td="bgcolor:#CCFFCC"]
0.221​
[/td][td="bgcolor:#CCFFFF"]
0.079​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
21​
[/td][td]
19​
[/td][td]
-0.309​
[/td][td="bgcolor:#CCFFCC"]
0.279​
[/td][td="bgcolor:#CCFFFF"]
0.058​
[/td][td][/td][td][/td][/tr]
[tr][td="bgcolor:#C0C0C0"]
22​
[/td][td]
20​
[/td][td]
0.000​
[/td][td="bgcolor:#CCFFCC"]
0.309​
[/td][td="bgcolor:#CCFFFF"]
0.030​
[/td][td][/td][td][/td][/tr]
[/table]


For other methods, see https://en.wikipedia.org/wiki/Numerical_differentiation
 
Last edited:
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