Automatic differentiation using dual numbers

[Thomas Klemm]

Example

Find the second negative maximum of \(\sin\left(\sqrt[3]{x}\right)\).

Code:

00 { 59-Byte Prgm }
01▸LBL "f'(x)"
02 MVAR "x"
03 RCL "x"
04 1
05 COMPLEX
06 STO "x"
07 XEQ "f(x)"
08 COMPLEX
09 STO "x"
10 RTN
11▸LBL "f(x)"
12 RCL "x"
13 3
14 XEQ "NROOT"
15 XEQ "SIN"
16 END

SOLVER

Select Solve Program
f'(x)

-150 x
x=-150

-50 x
x=-50

x
-104.6461837960118930922325633514673

Exact value: \(\left(-\frac{3\pi}{2}\right)^3 \approx -104.6462\)