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y =
fun(
x)
const AD<
Base> &
x
const VecAD<
Base>::reference &
x
AD<
Base>
y
acos
,
asin
,
atan
,
cos
,
cosh
,
exp
,
log
,
log10
,
sin
,
sinh
,
sqrt
,
tan
.
Acos.cpp | The AD acos Function: Example and Test |
Asin.cpp | The AD asin Function: Example and Test |
Atan.cpp | The AD atan Function: Example and Test |
Cos.cpp | The AD cos Function: Example and Test |
Cosh.cpp | The AD cosh Function: Example and Test |
Exp.cpp | The AD exp Function: Example and Test |
Log.cpp | The AD log Function: Example and Test |
Log10.cpp | The AD log10 Function: Example and Test |
Sin.cpp | The AD sin Function: Example and Test |
Sinh.cpp | The AD sinh Function: Example and Test |
Sqrt.cpp | The AD sqrt Function: Example and Test |
Tan.cpp | The AD tan Function: Example and Test |
\[
\begin{array}{lcr}
\D{[ {\rm acos} (x) ]}{x} & = & - (1 - x * x)^{-1/2}
\end{array}
\]
\[
\begin{array}{lcr}
\D{[ {\rm asin} (x) ]}{x} & = & (1 - x * x)^{-1/2}
\end{array}
\]
\[
\begin{array}{lcr}
\D{[ {\rm atan} (x) ]}{x} & = & \frac{1}{1 + x^2}
\end{array}
\]
\[
\begin{array}{lcr}
\D{[ \cos (x) ]}{x} & = & - \sin (x) \\
\D{[ \sin (x) ]}{x} & = & \cos (x)
\end{array}
\]
\[
\begin{array}{lcr}
\D{[ \cosh (x) ]}{x} & = & \sinh (x) \\
\D{[ \sin (x) ]}{x} & = & \cosh (x)
\end{array}
\]
\[
\begin{array}{lcr}
\D{[ \exp (x) ]}{x} & = & \exp (x)
\end{array}
\]
\[
\begin{array}{lcr}
\D{[ \log (x) ]}{x} & = & \frac{1}{x}
\end{array}
\]
\[
\begin{array}{lcr}
{\rm log10} (x) & = & \log(x) / \log(10)
\end{array}
\]
\[
\begin{array}{lcr}
\D{[ \sin (x) ]}{x} & = & \cos (x) \\
\D{[ \cos (x) ]}{x} & = & - \sin (x)
\end{array}
\]
\[
\begin{array}{lcr}
\D{[ \sinh (x) ]}{x} & = & \cosh (x) \\
\D{[ \cosh (x) ]}{x} & = & \sinh (x)
\end{array}
\]
\[
\begin{array}{lcr}
\D{[ {\rm sqrt} (x) ]}{x} & = & \frac{1}{2 {\rm sqrt} (x) }
\end{array}
\]
\[
\begin{array}{lcr}
\tan (x) & = & \sin(x) / \cos(x)
\end{array}
\]