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KhiCAS Ableitungen

Ableitung Trinkgeld

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#1 naluca

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Posted 23 February 2023 - 09:23 PM

Hallo,

ich habe  mir Khicas auf meinen Taschenrechner (fx-CG50) heruntergeladen, um  von einer Funktion die erste Ableitung zu bilden. Ich weiß nicht genau, wie ich jetzt die Funtkion eintippe und  der Taschenrechner mit die Ableitung anzeigt bzw auch am besten direkt zusammenfasst. Falls sich jemand damit auskennt, gerne bitte melden. Als Belohnung gebe ich auch ein kleines Trinkgeld.

Vielen lieben DANK!



#2 HappyCalc

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Posted 24 February 2023 - 12:38 PM

In KhiCAS you can either enter expressions in inline notation or mathematical notation.
KhiCAS will normally start in the inline mode. But you can enter the mathematical mode by pressing F3 (view).

As an example, I will use 2x³ + x²

To create a function, you can either enter

<expression>=><name>
2*x^3+x^2=>f

or

<name>:=<expression>
f:=2*x^3+x^2

or

<name>(<variable>):=<expression>
f(x):=2*x^3+x^2

then you can enter

<expression>'
f'

or if you used an other variable than x

diff(<expression>,<variable>)
diff(f,x)

that will result in

2*3*x^2+2*x

to simplify this, you can use

<expression>=>/

or

simplify(<expression>)

then you'll get

6*x^2+2*x

which is the derivative of 3x^3+2x^2. Great!

To sum up:

f:=3*x^2+x^2
fd:=f'=>/

fd will contain the derivative now.

 

If you used

f(x):=2*x^3+x^2

results will look different:

(x)->6*x^2+2*x

the (x)->... means, that you can use f(x) like a normal function:

You can calculate f(5) by just typing it in.
If you didn't use f(x):=..., you can calculate f(5) by typing

f(x=5)

You can enter the arrow '=>' by pressing the :->: button, the apostrophe ' by pressing F2 (calc) 1. The only way i know to get the colon ':' is by pressing Shift DEL and selecting it by hand. (There was another way in an earlier version, but I guess it was removed).

I hope that helps! :yawn:

(And I don't need a tip, I'm happy if I can help people with calculator stuff)


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#3 naluca

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Posted 24 February 2023 - 10:59 PM

In KhiCAS you can either enter expressions in inline notation or mathematical notation.
KhiCAS will normally start in the inline mode. But you can enter the mathematical mode by pressing F3 (view).

As an example, I will use 2x³ + x²

To create a function, you can either enter

<expression>=><name>
2*x^3+x^2=>f

or

<name>:=<expression>
f:=2*x^3+x^2

or

<name>(<variable>):=<expression>
f(x):=2*x^3+x^2

then you can enter

<expression>'
f'

or if you used an other variable than x

diff(<expression>,<variable>)
diff(f,x)

that will result in

2*3*x^2+2*x

to simplify this, you can use

<expression>=>/

or

simplify(<expression>)

then you'll get

6*x^2+2*x

which is the derivative of 3x^3+2x^2. Great!

To sum up:

f:=3*x^2+x^2
fd:=f'=>/

fd will contain the derivative now.

 

If you used

f(x):=2*x^3+x^2

results will look different:

(x)->6*x^2+2*x

the (x)->... means, that you can use f(x) like a normal function:

You can calculate f(5) by just typing it in.
If you didn't use f(x):=..., you can calculate f(5) by typing

f(x=5)

You can enter the arrow '=>' by pressing the :->: button, the apostrophe ' by pressing F2 (calc) 1. The only way i know to get the colon ':' is by pressing Shift DEL and selecting it by hand. (There was another way in an earlier version, but I guess it was removed).

I hope that helps! :yawn:

(And I don't need a tip, I'm happy if I can help people with calculator stuff)

Vielen Dank! Ich habe deine Schritte sehr gut verstanden. Weiß du, wie ich das alles also erste Ableitung inklusive zusammenfassen in einen Befehl machen kann den ich direkt auswählen kann (eventuell im Menü)? Falls das nicht geht, wollte ich dich fragen, ob man die Funktionen auch noch besser zusammenfassen/ vereinfach kann mit Klammern. Ein sehr einfaches  Beispiel: f(x)= x^3  --> f(x)= x(x^2)



#4 HappyCalc

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Posted 25 February 2023 - 03:54 PM

You can always calculate the derivative of the function directly like that:

(2*x^3+x^2)'=>/

If you instead of simplifying the result want to factorize it, use =>* instead:
 

f'=>*
(2*x^3+x^2)'=>*

which will result in

2*x*(x^2+1)


#5 pan.gejt

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Posted 25 February 2023 - 09:17 PM

You can enter the assignment operator ":=" by pressing shiftarrow.jpg button


Edited by pan.gejt, 25 February 2023 - 09:18 PM.


#6 naluca

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Posted 28 February 2023 - 08:34 PM

 

You can always calculate the derivative of the function directly like that:

(2*x^3+x^2)'=>/

If you instead of simplifying the result want to factorize it, use =>* instead:
 

f'=>*
(2*x^3+x^2)'=>*

which will result in

2*x*(x^2+1)

Hallo, vielen Dank. Jedoch zeigt der mir bei einer E Funktion häufig einen Bruch an, geht das auch ohne Bruch?



#7 HappyCalc

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Posted 11 March 2023 - 05:26 PM

Yes, you can use the approx() function to calculate an approximate result:

approx(e^3)
20.0855369

You can find it in the menu "real" Shift F2



#8 critor

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Posted 12 March 2023 - 08:14 PM

Hallo @naluca.

 

 

To get a summary of everything, maybe you could try :

tabvar(2*x^3+x^2)

gyilZXY.pngwdxw83V.png

 

But tabvar is only available if you installed the full version of KhiCAS for the fx-CG50 :

https://www-fourier....io/khicasio.zip






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