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z = x Op y
AD<Base> or
VecAD<Base>::reference
.
| Op | Meaning |
+ | z is x plus y |
- | z is x minus y |
* | z is x times y |
/ | z is x divided by y |
AD<Base> or VecAD<Base>::reference.
const Type &x
where Type is
VecAD<Base>::reference,
AD<Base>,
Base, or
double.
const Type &y
where Type is
VecAD<Base>::reference,
AD<Base>,
Base, or
double.
Type z
where Type is
AD<Base>.
| Add.cpp | AD Binary Addition: Example and Test |
| Sub.cpp | AD Binary Subtraction: Example and Test |
| Mul.cpp | AD Binary Multiplication: Example and Test |
| Div.cpp | AD Binary Division: Example and Test |
f
and
g
are
Base functions
\[
\D{[ f(x) + g(x) ]}{x} = \D{f(x)}{x} + \D{g(x)}{x}
\]
\[
\D{[ f(x) - g(x) ]}{x} = \D{f(x)}{x} - \D{g(x)}{x}
\]
\[
\D{[ f(x) * g(x) ]}{x} = g(x) * \D{f(x)}{x} + f(x) * \D{g(x)}{x}
\]
\[
\D{[ f(x) / g(x) ]}{x} =
[1/g(x)] * \D{f(x)}{x} - [f(x)/g(x)^2] * \D{g(x)}{x}
\]