# Re: [R] Obtain gradient at multiple values for exponential decay model

```> On Apr 6, 2018, at 8:03 AM, David Winsemius <dwinsem...@comcast.net> wrote:
>
>
>> On Apr 6, 2018, at 3:43 AM, g l <gnuli...@gmx.com> wrote:
>>
>>> Sent: Friday, April 06, 2018 at 5:55 AM
>>> From: "David Winsemius" <dwinsem...@comcast.net>
>>>
>>>
>>> Not correct. You already have `predict`. It is capale of using the
>>> `newdata` values to do interpolation with the values of the coefficients in
>>> the model. See:
>>>
>>> ?predict
>>>
>>
>> The ยง details did not mention interpolation explicity; thanks.
>>
>>> The original question asked for a derivative (i.e. a "gradient"), but so
>>> far it's not clear that you understand the mathematical definiton of that
>>> term. We also remain unclear whether this is homework.
>>>
>>
>> The motivation of this post was simple differentiation of a tangent point
>> (dy/dx) manually, then wondering how to re-think in modern-day computing
>> "homework"). :)
>>
>> Personal curiosity should be considered "homework".
>
> Besides symbolic differentiation, there is also the option of numeric
> differentiation. Here's an amateurish attempt:
>
> myNumDeriv <- function(x){ (exp( predict (graphmodeld,
> newdata=data.frame(t=x+.0001))) -
>                                            exp( predict (graphmodeld,
> newdata=data.frame(t=x) )))/
>                                          .0001 }
> myNumDeriv(c(100, 250, 350))```
```
I realized that this would not work in the context of your construction. I had
earlier made a more symbolic version using R formulae:

0,100
40,78
80,59
120,38
160,25
200,21
240,16
280,12
320,10
360,9
400,7')
graphmodeld<-lm(log(c)~t, graphdata)
graphmodelp<-exp(predict(graphmodeld))
plot(c~t, graphdata)
lines(graphdata[,1],graphmodelp)
myNumDeriv(c(100, 250, 350), graphmodeld )
#----------------------------------------------
1           2           3
-0.31464102 -0.11310753 -0.05718414

>
>
>
> David Winsemius
> Alameda, CA, USA
>
> 'Any technology distinguishable from magic is insufficiently advanced.'
> -Gehm's Corollary to Clarke's Third Law
>
> ______________________________________________
> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
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> and provide commented, minimal, self-contained, reproducible code.

David Winsemius
Alameda, CA, USA

'Any technology distinguishable from magic is insufficiently advanced.'
-Gehm's Corollary to Clarke's Third Law

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