Automatic differentiation using dual numbers

[Thomas Klemm]

(06-19-2022 02:23 AM)lrdheat Wrote:  what if an nRoot(x) appeared within a larger equation such as 3Root(x) +X^2 -3*(x/5)

Example

Find the minimum of \(\sqrt[3]{x}+x^2-\frac{3x}{5}\).

We can keep f'(x) and simply adjust f(x):

Code:

11▸LBL "f(x)"
12 RCL "x"
13 3
14 XEQ "NROOT"
15 RCL "x"
16 XEQ "X↑2"
17 +
18 RCL "x"
19 3
20 ×
21 5
22 ÷
23 -
24 END

SOLVER

Select Solve Program
f'(x)

-1 x
x=-1

0 x
x=0

x
-0.1952345627907014530751112228253494

-0.1952345627907014530751112228253494266891 from Solve[D[Surd[x,3]+x^2-3x/5,x]=0]