Derivatives on HP 42S

[Thomas Klemm]

(08-26-2018 04:47 PM)lrdheat Wrote:  Why is dx successful in solve, but not as a means to find dx of a specific x value?

(08-21-2018 12:34 AM)Thomas Klemm Wrote:  For a small discrete h, this can be approximated by

\(\frac{\partial f}{\partial x}\approx\frac{\Im[f(x + ih)]}{h}\)

Since we search for stationary points we set:

\(\frac{\partial f}{\partial x}=0\)

Which we approximate with just:

\(\Im[f(x + ih)]=0\)

To return an approximation for the derivative we have to divide \(\Im[f(x + ih)]\) by \(h\):

Code:

LBL "dF"
MVAR "x"
MVAR "h"
RCL "x"
RCL "h"
COMPLEX
XEQ "Fx"
COMPLEX
RCL÷ "h"
END

With your example:

Code:

LBL "Fx"
SIN
END

We can calculate the value of \(\frac{d}{dx}\sin(x)\) at \(x=1\):

1E-6
STO "h"
1
STO "x"
XEQ "dF"

x: 5.40302305868e-1

Compare this with \(\cos(1)\):

1
COS

x: 5.40302305868e-1


Best regards
Thomas