Saturday, December 4, 2021

HP 17B and HP 27S: Derivatives to the Nth Order (and TI-84 Plus CE Python 5.7 update)

 HP 17B and HP 27S: Derivatives to the Nth Order


With the Solver of the HP 17B family, HP 27S, and the HP 19B calculator, we can calculate derivatives of any order.  Four derivatives are presented here.  You can use any name you want other than those presented here.  Each derivative is to the kth order. 


Derivative 1:   d^k/dx^k a × x^n 


N and K must be positive integers, D is the value of the derivative  


DER1: D=A×X^(N-K)×PERM(N:K)


Example:

Input:  N = 2, K = 1, A = 3, X = 1.5

Result:  D = 9


Derivative 2:   d^k/dx^k e^(a × x) 


K must be a positive integer, D is the value of the derivative


DER2: D=A^K×EXP(A×X)


Example:

Input:  A = 1.8, K =3, X = 3

Result:  D = 213.4409


Derivatives 3 and 4 will require trigonometric functions, which are not available on the HP 17B family.   It is recommended you set the calculator to Radian angle mode.


Derivative 3:  d^k/dx^k sin(a × x)


DER3: D=IF(MOD(K:2)=0:(-1)^(K÷2)×A^K×SIN(A×X):(-1)^((K+3)÷2)×A^K×COS(A×X))


Examples:

Input:  A = 0.75, X = 0.66, K = 2

Result: D = -0.2672


Input:  A = 0.75, X = 0.66, K = 3

Result: D = -0.3712


Derivative 4:  d^k/dx^k cos(a × x)


DER4: D=IF(MOD(K:2)=0:(-1)^(K÷2)×A^K×COS(A×X):(-1)^(K÷2+1÷2)×A^K×SIN(A×X))


Examples:

Input:  A = 0.75, X = 0.66, K = 2

Result: D = -0.4950


Input:  A = 0.75, X = 0.66, K = 3

Result: D = 0.2004


Eddie


All original content copyright, © 2011-2021.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 


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