Numerical derivative of an analytical function - Google sheets

For this case I shall refer the reader to a previous post on the backgroung about derivatives. There you will find some basic details about what is being exposed here.

Let us estimate the first derivative of the smooth function,

$f(x)=4x^4+8x^3-x+9$

between $x=0$ and $x=10$. For this we shall use,

$f'(x_i)=\frac{f\left(x_{i+1}\right)-f(x_i)}{|x_i-x_{i+1}|}$     

Next, error or validation of the previous approximation can be easily checked since we already know that,

$f'(x)=16x^3+24x^2-1$

Some people talk about constant step:

$h=|x_i-x_{i+1}|$ 

but this explicit way is better since it allows to account for not so smooth variations of $f(x)$.

These calculations were already performed in the following Google Sheet:

Numerical derivative of a function 

where three different steps were used $h=1, 0.5, 0.1$. Notice, that the % error decreases with the step. Then, as you may notice error decreases with $h$.

Any questtion? Write in the comments and I shall try to help.

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Ildebrando.