Robert Smith avatar Robert Smith committed 9bf14e9

give example of derivative computation using dual numbers

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       (dual (expt a b)
             (+ (* p b (expt a (1- b)))  ; Factor out aᵇ?
                (* q (log a) (expt a b)))))))
+;;; To evaluate the derivative of f at x, compute f(〈x, 1〉) and the
+;;; result will be 〈f(x), f′(x)〉.
+;;; For example, √sin(x) can be computed by
+(defun sqrt-sin (x)
+  (dual-sqrt (dual-sin (dual x 1))))
+;;; The derivative at x=3 is -1.317... and our computation gives...
+;;;   CL-USER> (sqrt-sin 3.0)
+;;;   #<0.37565944 - 1.3176728ε>
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